CA1205214A - Method and computer tomography device for determining a tomographic image with elevated resolution - Google Patents
Method and computer tomography device for determining a tomographic image with elevated resolutionInfo
- Publication number
- CA1205214A CA1205214A CA000427539A CA427539A CA1205214A CA 1205214 A CA1205214 A CA 1205214A CA 000427539 A CA000427539 A CA 000427539A CA 427539 A CA427539 A CA 427539A CA 1205214 A CA1205214 A CA 1205214A
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- CA
- Canada
- Prior art keywords
- measuring
- subgroup
- measuring data
- paths
- radiation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/006—Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2211/00—Image generation
- G06T2211/40—Computed tomography
- G06T2211/421—Filtered back projection [FBP]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10S—TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10S378/00—X-ray or gamma ray systems or devices
- Y10S378/901—Computer tomography program or processor
Abstract
ABSTRACT:
Method and computer tomography device for determining a tomographic image with elevated resolution.
The invention relates to a computer tomography device, in which the row of detectors has been rotated through the quarter of a detector angle (.DELTA.?/4) with respect to the X-ray source. The invention proposes to filter (or convolute) the selected parallel measurement values measured in a given direction instead of doing so with all the se-lected measurement values measured in parallel and anti-parallel directions. Although a loss then occurs for the information in the range of higher frequencies, this loss is not significant. Due to the frequency-limiting influences of the width of the measuring beam, interpolation in the backprojection device and image element size in the image matrix, the overall frequency response curve of the computer tomography device is not essentially worse. With the use of the present invention, however, the calculating time required for filtering is reduced by a factor 2 and the current measurement values can be processed in a simpler manner (pipeline processing).
Method and computer tomography device for determining a tomographic image with elevated resolution.
The invention relates to a computer tomography device, in which the row of detectors has been rotated through the quarter of a detector angle (.DELTA.?/4) with respect to the X-ray source. The invention proposes to filter (or convolute) the selected parallel measurement values measured in a given direction instead of doing so with all the se-lected measurement values measured in parallel and anti-parallel directions. Although a loss then occurs for the information in the range of higher frequencies, this loss is not significant. Due to the frequency-limiting influences of the width of the measuring beam, interpolation in the backprojection device and image element size in the image matrix, the overall frequency response curve of the computer tomography device is not essentially worse. With the use of the present invention, however, the calculating time required for filtering is reduced by a factor 2 and the current measurement values can be processed in a simpler manner (pipeline processing).
Description
2~9~
PHN.10.346 I 13.4.1983 Method and computer tomography device for de-termining a tomographic image with elevated resolution.
The invention relates to a computer -tomography device for determining a radia-tion at-tenuation distribution in a plane of a body, which device compri.ses:
- at least one source for producing a flat fan~
shaped beam of penetra-ting radiation, by means of which the body i9 irradiated from a multi-tude of directions passing through a central point and regularly distributed over 360 along a plurality of measuring paths diverging from I0 the source and located in the plane;
- a series of detectors for cletecting radiation passed through the body for supplying a group of measuring data for each direction, which are , a measure for the attenuation of the radiation ;~: IS in the body occurring along the plurality oE
diverging measuring paths, radiation emitted from the source and passing through the central ` : point striking a detector a-t the centre of a .
row spanned by the Ean-shaped beam halfway be-Q tween the centre and edge thereof and a measur-ing path having a maximum width a which i.s measured along a line which is at righ-t angles -to the measuring path and passes through the central point;
- a calculating device having = a memory for storing measuring data and for deriving Erom the groups of measuring data sub-groups oE measuring data, which have been measured along (imaginary) measuring pa-ths with the same direction;
= a filtering device :Eor carrying out a convolution or a Fourier transformation, -` ~%~5Z~
P~IN.10.346 2 13.~.19~3 a filtering and a Fourier back transformation of each subgroup of measuring data;
= a backprojection device for distributing and adding values of each subgroup of filtered measuring data respectively over and to a ma-trix of memory cells of the memory forming an i.mage matrix, = and a clisplay device for displaying the con-tent of the image matri~.
The invention further relates to a method of de-termini.ng a radiation attenuation d~stribution in a plane of a body, in which the body is irradiated from a multitude of directions passing through a central point and distributed ~: over 360 with a flat fan-shaped beam of pene-trating radi-5 ation ~iverging from a point for determining a group of measuring data ~or each measuring direction, which have been measured along a plurality of measuring paths located i.n the plane of the body and are a measure for the attenuation of .~; the radiation in the ~ody occurring along the plurality of n diverging measuring paths, an imaginary line passing through a central point enclosing in each direction a quarter of an ~ angle enclosed by two adjacent measuring paths with a central :~ measuring path, which has a maximum width a which is measured along a line whi¢h is at right angles to the 25 measuring path and passes through the central point, after ~ ~ which subgroups are derived from the groups of measuring :~ clata, which subgroups are measurecl along (imaginary) : measuring paths with the same measuring direction, whereupon each subgroup either through a convolution calculation or ~: through a ~ourier transformation, a filtering and a ~ourier back-transformation is fi.ltered and is backprojected onto an image ma-trix.
Such a method and compu-ter tomography device are known from the US-PS ~,051,379, in which the row of detectors is arranged asymmetrically -to a cen-tral line which passes through the cen-tral poin-t and -the X-ray radiation source in orcler -to increase -the resolu-tion. The measurlng ~a-ta which ~2~
PIIN.10.3L~6 3 13.~.1983 have been measured along parallel measuring paths (in opposite directions) overlapping each other in part, are combined in a subgroup and ~urther processed in the manner described, for example, in U~-PS 3,983,398. It is then re-quired to store the measuring data measured from the variousdirections be~ore they can be fur-ther processed. The radiat-ion source must have fulfilled such a large rotation about the central point that all the measuring data associa-ted with a subgroup of parallel (overlapping) measuring paths 10 are determined, after which the subgroup of measuring data can be filtered and backprojected. The increase o-f the re-solution is obtained by increasing the required storage space, by a delay at the beginning of the processing of the measuring data and by a larger number of calculating operations by doubling of the number of measuring pa-ths per subgroup.
The invention has for its object to provide a computer tomography device, in which a shorter waiting time ~ is required before the processing of -the measwring cda~-t/a is :-- s-tarted, the filtering is carried out much more-r~id~-(-factor 2) and an image with a high resolu-tion is obtained.
The computer tomography device according to the invention is therefore characterized in that the calculating device determines from the groups of measuring data measured over 360 for each measuring direction two subgroups of measuring data7 the measuring data of one subgroup being measured in a direction opposite -to tha-t in which the measuring data of the other subgroup are measured, while the distance between two measuring paths associa-ted wi-th two adjacen-t measuring data in a subgroup is at most a and larger -than 2 a, in -that the filtering device has a -fre-quency response curve wi-th a maximum ~or the frequency (2a) and zero points ~or the frequenci.es 0 and 1/a and in -that the backprojec-tion device dis-tributes and adds each pair o:~ ln-ter:Leaved subgroups o-f fil-terecl measuring cla-ta with an -in-terpola-tion dis-tance of (2a) respectively over and -to -the image ma-trix, the number of memory cells o:~ which 9~
,,. ~
P~N.10.3~6 L~ 13.L~.1983 is larger than the square of the number of detectors spanned by the beam of diverging radia-tion.
In the computer tomography device according to the invention, the filtering of a subgroup is already started as soon as the source has fulfilled with respec-t to the cen-tral point a rotation larger than the apical angle enclosed by the diverging beam of radiation; therefore, the storage of the groups of measuring data requires much less storage space (factor A). The filtering of the subgroups requires less calculating time (fac-tor 2) because the number of measuring data per subgroup has been halved. The filter-ing behaviour of -the computer tomography device is deter-mined by the frequency response curve of the (convolution) filtering device and the backprojection device. The frequency 5 response curve of the filtering device has zero points for the frequencies zero and 1/a, a being the maximum distance between two measuring paths in a subgroup, and has a maximum for the frequency(2a) . The filtering device, which accord-ing to the prior art filters simultaneously the measuring 20 clata, which have been measured along parallel and anti-parallel measuring paths, has a frequency response curve Q(R) which is determined by Q(R) = ¦R¦ for the frequency R ~ 1/a. If a linear interpolation is used, the backprojection device has a frequency response curve representecl by 25 sin c (~ 2 a.R), R being the frequency to be imaged in the image matrix; consequently, there is a zero point for -the ; frequency R = 2/a. The overall frequency trans~er function is de-termined by the produc-t of the two said frequency response curves It can also be recognized that 9 if the size of an image element is approximately equal to the maximum distance a be-tween the measuring paths, which is a practical choice, although the fil-tering device according to the prior ar-t permits a larger frequency range, the (high) frequencies to bc ultimately irnaged in the image ma-trix are considerably limitecl by -the frequency response c-urve of -the back projec-t:ion device and the fil-tering behaviour of the image ~05~
PHN.10.3~6 5 13.l~.1983 matrix. In the computer -tomography clevice according to the inven-tion, -the filtering device produces a considerable attenuatiorl O:r the high frequency, but, because the back-projection device passes these frequencies only in a strong-ly a-ttemla-tecl form, this is not a serious limita-tion of -the frequencies ultimately imaged in the image matrix. In the compu-ter tomography device according -to -the invention, an optimum high resolution is attained with a given number of de-tectors with a minimum calculating -time -to carry out the filtering ofthe measuring data and with a memory adapted to a minimum ex-tent with respect toits size.
The method according to the invention is charac-terized in that two subgroups areselected from the groups of measuring data for each measuring direction, measuring da-ta of the ~irst subgroup being de-termined along measuring paths which are antiparallel to measuring paths along which the measuring data of the second subgroup are determined, in each subgroup the distance between two measuring paths being at most a and large~than 2a and filtering of each subgroup being carried out with a filtering device, the frequency response curve of which has a maximum for the frequency ~2a) and zero points for the frequencies zero and 1/a, after which each first subgroup of filtered measuring data is interleaved with the measuring data of the associated second subgroup and -the interleaved sub-groups of measuring data are backprojected, an inter-polation distance between the measuring data being (2a) The invention will be described with reference to embodiments shown in the drawing, in which:
Figure 1 shows diagrarnmatically a computer tomo-graphy device according to -the invention, Figure 2 shows the principle of -the measuring arrangement of the device shown in Figure 1, Figure 3 shows frequency response curves of a fil-tering device for computer tomography devices, Figure l~ shows frequency response curves of different backprojec-t:Lon devices, and 52~4~
.
PIIN.1O.346 6 13.4.1983 ~ igures 5a and 5b show frequency response curves of a computer tomography device according to the invention and of such a device according to -the prior art.
~ computer tomography device of the kind shown diagrammatically in ~igure 1 comprises a radiation source 1, which may p.eferably be an X-ray tube, for producing a flat beam 3 o~ X-ray radiation to be diaphragmed by a diaphragm 2 and diverging through an angle ~ , which beam may have a thickness of 3 to 35 mm. The radia-tion beam 3 is incident upon a row 4 o~ separate detectors 5, which measure each radiation reaching -the relevant detector 5 through a measuring path 3a. The width of a measuring pa-th ancl the relative distance of the measuring paths de-termine the spatial accuracy with which an object 7 lying on a table 6 is scanned and is constructed. In order to increase this accuracy (resolution) 7 the detector row 4 is arranged asymmetrically to a central ray 8, which passes from -the source 1 through a central point 9 (of rotation).
In a preferred embodiment, the central ray 8 20 strikes a detector 5 (see fig. 2) at the centre of the row 4 halfway between the cen-tre and the edge of the detector 5, so that ~ of the detector 5 lies on one side and ~ of this detector on the other side of the cen-tral ray 8.
The detector row 4 comprises, for example, 576 de-tectors 5, 25 ~ being = 43.2 and the dis-tance between the source 1 and the detector row 4 amounting to 1 mO The row 4 of detectors 5 may be composed, for example, of an elongate gas-filled ionization chamber, in which flat electrodes are arranged in a row parallel to each other.
The assembly of` radiation source 1 and detector row 4 is mounted on a supporting frame 10 which is arranged so as to be rotatable about thc central point 9 so that a layer of the object 7 can be irradiated in diff`erent directions (lying in one plane) wi-th the radiation beam 3.
35 The supporting ~rame 10, which is guided l~ith -the aid of boar:ings 11, is driven by means of a mo-tor 13 in a -trans-mission gear 12. The drive may be con-t:inuous, but also ~ s~
PHN.10.346 7 13.4.1983 intermi-ttent, the radiation source 1 emi-tting in the firs-t case preferably a radiation pulse.
The detectors 5 supply measuring signals whieh are applied through an amplifier 1l~ to a signa] eonverter 15, in which the measuring signals are digitized, after whieh the signals are supplied to a ealeulating deviee 16.
The measuring signals are corrected by the caleulating de-viee 16 for "offse-t", logarithmized and calibrated with reference to logari-thm and calibration tables present in a memory 17, after whieh the measuring values are stored in the memory 17. An image matrix of the radiation attenuation clistribution to be determined by -the ealeulating deviee 16, in whieh the measuring data are proeessed by a filtering deviee 16a, whieh earries out either a eonvolution or a 15 Fourier transformation, a filtering and a baektransformation, and then by a baek-projeetion deviee 16b, whieh distributes the filtered measuring data over memory cells of an image ma-trix stored in the memory 17, can be displayed on a dis-play device 18 tmonitor).
A counter 19 eounts the number of pulses whieh is generated by a pulse generator 20 during rotation of the supporting frame 10 so that a counter position of the coun-ter 19 is a measure for the orien-tation of the supporting frame 10 and henee is a measure for the angular rotation e 25 of the successive measuring direetions.
It has proved advantageous to choose the dis-tance between -the radiation souree I and -the objeet 7 so that it can be adapted to the size of the objec-t 7. Therefore, -the radiation source 1 and the deteetor row ~ are moun-ted on a 30 support 21, which can be displaced along guiding rails 22 on bearings 23 ancl by means of a transmission gear 25 coupled with a mo-tor 2~. By means of a swi-tch 27, the motor 24 can be driven through a control circui-t 26.
For the sake of clarity9 in Figure 2 the arrange-ment of radia-tion souree I and de-tector row ~ is shown in an x - y co-ordlnate system. The measurement value to be supp:L-Led by -the detec-tor 5i in -the position shown is assumed ~2~S~
- ` PHN.10,346 8 13.4.1983 to be measured along a measuring path 30a which passes through the source 1 and the cen-tre of the detector ~i.
The distallce between the measuring paths at the area of the central point 9 is ~= r. ~9 r being the distance between the source 1 and the central point 9 and~being the angle en-closed between -two measuring pa-ths. It can be recognized tha-t a:~ter rotation o~ the source I with detectors 5 throi1gh an angle~ ~ in the direction 0 the measuring path associa-ted ~ith a measurement value and situated between the source 1 and the detector 5i~1 is parallel to -the measuring path between the source 1 and the detector 5i before the rotation l~as ful~illed. It can be recognized that from the groups o~
measuring signals measured in the dif~erent positions i subgroups o~ measuring signalscan be selec-ted which are 15 measured along parallel paths. The distance between two ad-jacent paths amounts to r.cos ~ i being the angle enclosed by the central ray 30 and the connection line 30 between the source 1 and a detector 5i. Such a subgroup is filtered with the aid of the calculating de-vice 16 20 (Figure 1), the filtering curve of a filter Q(R) having a cut-off frequency Rmax of (2a) and may have a ~orm as indicated in Figure 3 by a straight line 31.
In Figure 3~ the spatial frequency is plotted on the abscissa and the amplitude o~the (convolution) filter 25 Q(R) is plotted on -~he ordinate. The example shGwn in Figure 3 o~ a ~requency response curve 31 (cut-off frequency (2a) ) o~ a filtering action of the calcula-ting device 16 according to the prior art is described, for example, in g'Indian Journal of Pure and Applied Physics", ~ol.9, November 1971, pp. 997-1003. The curves 31 and 33 sho1~n in Figure 3 are parts of periodical func-tions resulting ~rom a discreet Fourier trans~ormation. These functions be described more fully hereinafter. The filtering to be effected should be tuned -to the sampling frequency and :is cle-te~rrnined by the d:istance a be-tween -the measuring pa-ths and is inversely propor-tional thereto. I-t should be appre-cia-ted that -thereby a:Lso the resolu-tion o~ -the irnage -to be recons-tr-uc-ted ofan objec-t 7 is defined.
-~ ~%~s~
PHN.10,346 9 13.4.1983 In order to increase -the resolution, it has al-ready been suggested -to arrange the detector row L~
asymmetrically to the central ray 30 (Figure 2~ of the source 1, while this ray, passing through the central point 9, strikes the detec-tor 5i~ ~ of the detector 5i lying on one side Or -the central ray 30 and the remaining l part of the de-tector 5i on the o-ther side of the ray 30. The pro-posed asymmetrical arrangement of the detector 5i is obtained by rotation through a quarter of the aperture angle ~ ~/4) of a detec-tor 5i' the source 1 being the centre of this rotation. The detector 5 supplies a measurement value measured along a measuring path 30a. After a rotation of the source 1 and the detector row L~ through an angle ~
of 180, the detector 5i supplies a measurement value asso-ciated with -the measuring path 30b. The measuring paths 30a and 30b are parallel and have a relative clistance a/2 (at the area of the centre of rotation 9)0 It should be appre-ciated that from the groups of measurement values (deter-minative in the different source positions ~i and ei ~ 180) subgroups of measuremen-t values can be selected, -the dis-tance between two adjacen-t measuring paths being a.cos ~ /2. According to the aforementioned publications, such a subgroup is allowed to be filtered by a filter Q(R), the response curve 33 of which is indicated by a broken line in Figure 3. The cut-of~ ~requency is in -this case I/a, ;~ which would mean a doubling of the resolution. On the other hand, i a large memory is required to store all the measure-men-t values (these are a-t least 250 x 223 measurement values of the number of detectors is 250 and the number of source positions is i 180 for a rotation of 180 ); ii the filter-ing canno-t be started until all the required measurement values have been stored and selected (dura-tion a few seconds) and iii -the required calculating operations for the filtering are cloublecl and consequently require a longer caLculating timo or a larger calculating capacity.
In Figure 3, the ~requency response curve Q(R) of a til-tering by -the calc1l:La-ting device according -to the :~%~52~
PHN.10,3~6 10 13.L~.1983 invention is indicated by lines 31 and 31'. In the filtering according to -the invention, the measuremen-t values of a sub-group wi-th the same measuring direction are also processecl.
The subgroup of measuring signals to be fil-ter is measured 5 along measuring paths which have a relative dis-tance a = (r.cos~ y). A second subgroup, which ls measured in the opposite direction, is consequently not interleaved wi-th -the first subgroup before -the filterlng. The filtering can thus be started as soon as the source I (Figure 2) has been lO rotated through an angle 0 = ~(apical angle of radiation beam) because then all the measurement values of a firs-t subgroup have already been measured. The first filtered sub-groups are stored until -the associated second subgroups have been measured and filtered, after which the first subgroup 15 and the associated second subgroup are interleaved (the filtered measurement value of a subgroup is in a posi-tion be-tween two measurement values of the other subgro-up). Such a composi-te overall group consequently would also be obtained if the measurement values had been interleaved before the 20 filtering and had been processed by means of a filter, -the response curve of which is indicated in Figure 3 by lines 31 and 31'. This can be seen as follows. ~ group of measure-ment values obtained according to the prior art (rela-tive ; distance is filtered with fil-tering coefficien-ts (group I) 25 fO, f1, f2, --fN~ fN being -the Nyquist frequency and being determined by (2a) (straight line 31 in Figure 3). If the distance between the measurement values shoulcl be 20a, the Nyquist frequency is 1/a (straight line 33~ Figure 3).
If now a first subgroup of measurement values is filtered 30 according to the invention with the coefficients f ' f1' f2' ... fN and if afterwards a subgroup filtered in -the same manner is interleaved therewi-th, the subgroups in fac-t have been fil-tered wi-th -the coefficien-ts f , 0, f1, 0, f2, ~ ... fN, -the Nyquis-t frequency fN being 1/a and the 35coefficients f1 ~ f2~ e-tc. being associated wi-th frequencies which are two -tirnes h:igher -than the frequenc:ies associated wi-th -the coefficien-ts f1, f2 e-tc of -the group I .
~%~5~
PHN.10,346 11 13.4.1983 Alter having been interleaved, the filtered measurement values are backprojected in a manner known . It should be noted -that in -this case the first filtered subgroups of measuring signals should be stored, wllich requires storage space and waiting time. The back-projection of the first two interleaved subgroups can be started as soon as the second subgroup (antiparallel -to the first subgroup) has been composed and filtered. However, the speed at which such a second subgroup is filtered is four times higher than in case the subgroups should have been interleaved before the filtering (twice -the number of measuring data and twice the number of filtering coeffi-cien-ts) The gain to be achieved consists in that the sub-groups (still to be fil-tered are processed more rapidly, which can be effected simultaneously during the back-projection of subgroups of measuring data already filtered beforehand and subsequently interleaved.
However, in principle it is also possible -that each fil-tered subgroup is backprojected without beîng inter-Z0 leavecl with an associated filtered subgroup. Between each pair of filtered measurement values of each subgroup the values "0" should then be interposed. It is clear that in this case the overall calculating time for carrying out the backprojec-tion is doubled.
The ultimately ob-tained information in the image matrix then has been subjected to an overall frequency filtering which is the product of the frequency response curves of the filtering device, of the back-projection device and of the image matrix.
If the filtered measurement values -to be back-projec-ted are subjected to a linear interpolation, in fac-t a convolu-tion of a -triangular func-tion (having a base wid-th a) is carried out on the E`iltered measurement values (with -a distance of a/2). A convolution in the spatial range can 35 a:Lso be considered as a filtering l~i-th a filter T(R) in the E`requency range. The aforemen-tioned -triangular func-tion has a frequency response curve wllich is de-terminecl by T(R) = sinc (~ a.R). In F:igure 4 this curve is indica-ted ~052~9~
PHN.1o~3~l6 12 13.4.1983 by a line ~5, I-t should be appreciated that (linear) inter-polations in -the backprojection oP -the filtered measurement values lead to an essential unavoidable attenuation of the higher spa-tial frequencies.
The Eiltered measurement values are bac~projected onto an image matrix. It should be apprecia-ted that the size of the image elements of which the image matrix is composed is also de-terminative of the maximum spatial frequency -to be imaged. I~ the size of a (square) image element is P, -the frequency response curve of the image matrix is the Fourier transform G(R) of the block "P" is:
G(R) = sinc(~.P.R.). In Figure 4 the frequency response curve 41 of the image ma-trix with a size P of the image elemen-ts is shown, the distance P being assumed to be equal 5 -to the value a. If -the image matrix has an image element size of 2P, this image matrix has a frequency response curve G~R).sinc(-,~.P,R/2) indicated by a broken line l~3.
Such an image ma-trix requires a memory having a four times larger number of memory cells.
If the measurement values of the antiparallel subgroups are interleaved before the filtering (wi-th a cut-off frequency 2/a~ curve 33, Figure 3) and are backprojected af-ter filtering (filter T(R) = sinc (~.a/2oR)) in an image matrix having an image element size 2a (curve 43, G(R) =
25 sinc(l~a.R) 9 (Figure 4), the overall response curve t~ill have a variation as indicated by -the broken line 51a in Figure 5a. The overall filtering behaviour of -the computer tomography- device is de-termined by the product F(R) = Q(R).T(R).G(R) of the frequencyresponse curves of
PHN.10.346 I 13.4.1983 Method and computer tomography device for de-termining a tomographic image with elevated resolution.
The invention relates to a computer -tomography device for determining a radia-tion at-tenuation distribution in a plane of a body, which device compri.ses:
- at least one source for producing a flat fan~
shaped beam of penetra-ting radiation, by means of which the body i9 irradiated from a multi-tude of directions passing through a central point and regularly distributed over 360 along a plurality of measuring paths diverging from I0 the source and located in the plane;
- a series of detectors for cletecting radiation passed through the body for supplying a group of measuring data for each direction, which are , a measure for the attenuation of the radiation ;~: IS in the body occurring along the plurality oE
diverging measuring paths, radiation emitted from the source and passing through the central ` : point striking a detector a-t the centre of a .
row spanned by the Ean-shaped beam halfway be-Q tween the centre and edge thereof and a measur-ing path having a maximum width a which i.s measured along a line which is at righ-t angles -to the measuring path and passes through the central point;
- a calculating device having = a memory for storing measuring data and for deriving Erom the groups of measuring data sub-groups oE measuring data, which have been measured along (imaginary) measuring pa-ths with the same direction;
= a filtering device :Eor carrying out a convolution or a Fourier transformation, -` ~%~5Z~
P~IN.10.346 2 13.~.19~3 a filtering and a Fourier back transformation of each subgroup of measuring data;
= a backprojection device for distributing and adding values of each subgroup of filtered measuring data respectively over and to a ma-trix of memory cells of the memory forming an i.mage matrix, = and a clisplay device for displaying the con-tent of the image matri~.
The invention further relates to a method of de-termini.ng a radiation attenuation d~stribution in a plane of a body, in which the body is irradiated from a multitude of directions passing through a central point and distributed ~: over 360 with a flat fan-shaped beam of pene-trating radi-5 ation ~iverging from a point for determining a group of measuring data ~or each measuring direction, which have been measured along a plurality of measuring paths located i.n the plane of the body and are a measure for the attenuation of .~; the radiation in the ~ody occurring along the plurality of n diverging measuring paths, an imaginary line passing through a central point enclosing in each direction a quarter of an ~ angle enclosed by two adjacent measuring paths with a central :~ measuring path, which has a maximum width a which is measured along a line whi¢h is at right angles to the 25 measuring path and passes through the central point, after ~ ~ which subgroups are derived from the groups of measuring :~ clata, which subgroups are measurecl along (imaginary) : measuring paths with the same measuring direction, whereupon each subgroup either through a convolution calculation or ~: through a ~ourier transformation, a filtering and a ~ourier back-transformation is fi.ltered and is backprojected onto an image ma-trix.
Such a method and compu-ter tomography device are known from the US-PS ~,051,379, in which the row of detectors is arranged asymmetrically -to a cen-tral line which passes through the cen-tral poin-t and -the X-ray radiation source in orcler -to increase -the resolu-tion. The measurlng ~a-ta which ~2~
PIIN.10.3L~6 3 13.~.1983 have been measured along parallel measuring paths (in opposite directions) overlapping each other in part, are combined in a subgroup and ~urther processed in the manner described, for example, in U~-PS 3,983,398. It is then re-quired to store the measuring data measured from the variousdirections be~ore they can be fur-ther processed. The radiat-ion source must have fulfilled such a large rotation about the central point that all the measuring data associa-ted with a subgroup of parallel (overlapping) measuring paths 10 are determined, after which the subgroup of measuring data can be filtered and backprojected. The increase o-f the re-solution is obtained by increasing the required storage space, by a delay at the beginning of the processing of the measuring data and by a larger number of calculating operations by doubling of the number of measuring pa-ths per subgroup.
The invention has for its object to provide a computer tomography device, in which a shorter waiting time ~ is required before the processing of -the measwring cda~-t/a is :-- s-tarted, the filtering is carried out much more-r~id~-(-factor 2) and an image with a high resolu-tion is obtained.
The computer tomography device according to the invention is therefore characterized in that the calculating device determines from the groups of measuring data measured over 360 for each measuring direction two subgroups of measuring data7 the measuring data of one subgroup being measured in a direction opposite -to tha-t in which the measuring data of the other subgroup are measured, while the distance between two measuring paths associa-ted wi-th two adjacen-t measuring data in a subgroup is at most a and larger -than 2 a, in -that the filtering device has a -fre-quency response curve wi-th a maximum ~or the frequency (2a) and zero points ~or the frequenci.es 0 and 1/a and in -that the backprojec-tion device dis-tributes and adds each pair o:~ ln-ter:Leaved subgroups o-f fil-terecl measuring cla-ta with an -in-terpola-tion dis-tance of (2a) respectively over and -to -the image ma-trix, the number of memory cells o:~ which 9~
,,. ~
P~N.10.3~6 L~ 13.L~.1983 is larger than the square of the number of detectors spanned by the beam of diverging radia-tion.
In the computer tomography device according to the invention, the filtering of a subgroup is already started as soon as the source has fulfilled with respec-t to the cen-tral point a rotation larger than the apical angle enclosed by the diverging beam of radiation; therefore, the storage of the groups of measuring data requires much less storage space (factor A). The filtering of the subgroups requires less calculating time (fac-tor 2) because the number of measuring data per subgroup has been halved. The filter-ing behaviour of -the computer tomography device is deter-mined by the frequency response curve of the (convolution) filtering device and the backprojection device. The frequency 5 response curve of the filtering device has zero points for the frequencies zero and 1/a, a being the maximum distance between two measuring paths in a subgroup, and has a maximum for the frequency(2a) . The filtering device, which accord-ing to the prior art filters simultaneously the measuring 20 clata, which have been measured along parallel and anti-parallel measuring paths, has a frequency response curve Q(R) which is determined by Q(R) = ¦R¦ for the frequency R ~ 1/a. If a linear interpolation is used, the backprojection device has a frequency response curve representecl by 25 sin c (~ 2 a.R), R being the frequency to be imaged in the image matrix; consequently, there is a zero point for -the ; frequency R = 2/a. The overall frequency trans~er function is de-termined by the produc-t of the two said frequency response curves It can also be recognized that 9 if the size of an image element is approximately equal to the maximum distance a be-tween the measuring paths, which is a practical choice, although the fil-tering device according to the prior ar-t permits a larger frequency range, the (high) frequencies to bc ultimately irnaged in the image ma-trix are considerably limitecl by -the frequency response c-urve of -the back projec-t:ion device and the fil-tering behaviour of the image ~05~
PHN.10.3~6 5 13.l~.1983 matrix. In the computer -tomography clevice according to the inven-tion, -the filtering device produces a considerable attenuatiorl O:r the high frequency, but, because the back-projection device passes these frequencies only in a strong-ly a-ttemla-tecl form, this is not a serious limita-tion of -the frequencies ultimately imaged in the image matrix. In the compu-ter tomography device according -to -the invention, an optimum high resolution is attained with a given number of de-tectors with a minimum calculating -time -to carry out the filtering ofthe measuring data and with a memory adapted to a minimum ex-tent with respect toits size.
The method according to the invention is charac-terized in that two subgroups areselected from the groups of measuring data for each measuring direction, measuring da-ta of the ~irst subgroup being de-termined along measuring paths which are antiparallel to measuring paths along which the measuring data of the second subgroup are determined, in each subgroup the distance between two measuring paths being at most a and large~than 2a and filtering of each subgroup being carried out with a filtering device, the frequency response curve of which has a maximum for the frequency ~2a) and zero points for the frequencies zero and 1/a, after which each first subgroup of filtered measuring data is interleaved with the measuring data of the associated second subgroup and -the interleaved sub-groups of measuring data are backprojected, an inter-polation distance between the measuring data being (2a) The invention will be described with reference to embodiments shown in the drawing, in which:
Figure 1 shows diagrarnmatically a computer tomo-graphy device according to -the invention, Figure 2 shows the principle of -the measuring arrangement of the device shown in Figure 1, Figure 3 shows frequency response curves of a fil-tering device for computer tomography devices, Figure l~ shows frequency response curves of different backprojec-t:Lon devices, and 52~4~
.
PIIN.1O.346 6 13.4.1983 ~ igures 5a and 5b show frequency response curves of a computer tomography device according to the invention and of such a device according to -the prior art.
~ computer tomography device of the kind shown diagrammatically in ~igure 1 comprises a radiation source 1, which may p.eferably be an X-ray tube, for producing a flat beam 3 o~ X-ray radiation to be diaphragmed by a diaphragm 2 and diverging through an angle ~ , which beam may have a thickness of 3 to 35 mm. The radia-tion beam 3 is incident upon a row 4 o~ separate detectors 5, which measure each radiation reaching -the relevant detector 5 through a measuring path 3a. The width of a measuring pa-th ancl the relative distance of the measuring paths de-termine the spatial accuracy with which an object 7 lying on a table 6 is scanned and is constructed. In order to increase this accuracy (resolution) 7 the detector row 4 is arranged asymmetrically to a central ray 8, which passes from -the source 1 through a central point 9 (of rotation).
In a preferred embodiment, the central ray 8 20 strikes a detector 5 (see fig. 2) at the centre of the row 4 halfway between the cen-tre and the edge of the detector 5, so that ~ of the detector 5 lies on one side and ~ of this detector on the other side of the cen-tral ray 8.
The detector row 4 comprises, for example, 576 de-tectors 5, 25 ~ being = 43.2 and the dis-tance between the source 1 and the detector row 4 amounting to 1 mO The row 4 of detectors 5 may be composed, for example, of an elongate gas-filled ionization chamber, in which flat electrodes are arranged in a row parallel to each other.
The assembly of` radiation source 1 and detector row 4 is mounted on a supporting frame 10 which is arranged so as to be rotatable about thc central point 9 so that a layer of the object 7 can be irradiated in diff`erent directions (lying in one plane) wi-th the radiation beam 3.
35 The supporting ~rame 10, which is guided l~ith -the aid of boar:ings 11, is driven by means of a mo-tor 13 in a -trans-mission gear 12. The drive may be con-t:inuous, but also ~ s~
PHN.10.346 7 13.4.1983 intermi-ttent, the radiation source 1 emi-tting in the firs-t case preferably a radiation pulse.
The detectors 5 supply measuring signals whieh are applied through an amplifier 1l~ to a signa] eonverter 15, in which the measuring signals are digitized, after whieh the signals are supplied to a ealeulating deviee 16.
The measuring signals are corrected by the caleulating de-viee 16 for "offse-t", logarithmized and calibrated with reference to logari-thm and calibration tables present in a memory 17, after whieh the measuring values are stored in the memory 17. An image matrix of the radiation attenuation clistribution to be determined by -the ealeulating deviee 16, in whieh the measuring data are proeessed by a filtering deviee 16a, whieh earries out either a eonvolution or a 15 Fourier transformation, a filtering and a baektransformation, and then by a baek-projeetion deviee 16b, whieh distributes the filtered measuring data over memory cells of an image ma-trix stored in the memory 17, can be displayed on a dis-play device 18 tmonitor).
A counter 19 eounts the number of pulses whieh is generated by a pulse generator 20 during rotation of the supporting frame 10 so that a counter position of the coun-ter 19 is a measure for the orien-tation of the supporting frame 10 and henee is a measure for the angular rotation e 25 of the successive measuring direetions.
It has proved advantageous to choose the dis-tance between -the radiation souree I and -the objeet 7 so that it can be adapted to the size of the objec-t 7. Therefore, -the radiation source 1 and the deteetor row ~ are moun-ted on a 30 support 21, which can be displaced along guiding rails 22 on bearings 23 ancl by means of a transmission gear 25 coupled with a mo-tor 2~. By means of a swi-tch 27, the motor 24 can be driven through a control circui-t 26.
For the sake of clarity9 in Figure 2 the arrange-ment of radia-tion souree I and de-tector row ~ is shown in an x - y co-ordlnate system. The measurement value to be supp:L-Led by -the detec-tor 5i in -the position shown is assumed ~2~S~
- ` PHN.10,346 8 13.4.1983 to be measured along a measuring path 30a which passes through the source 1 and the cen-tre of the detector ~i.
The distallce between the measuring paths at the area of the central point 9 is ~= r. ~9 r being the distance between the source 1 and the central point 9 and~being the angle en-closed between -two measuring pa-ths. It can be recognized tha-t a:~ter rotation o~ the source I with detectors 5 throi1gh an angle~ ~ in the direction 0 the measuring path associa-ted ~ith a measurement value and situated between the source 1 and the detector 5i~1 is parallel to -the measuring path between the source 1 and the detector 5i before the rotation l~as ful~illed. It can be recognized that from the groups o~
measuring signals measured in the dif~erent positions i subgroups o~ measuring signalscan be selec-ted which are 15 measured along parallel paths. The distance between two ad-jacent paths amounts to r.cos ~ i being the angle enclosed by the central ray 30 and the connection line 30 between the source 1 and a detector 5i. Such a subgroup is filtered with the aid of the calculating de-vice 16 20 (Figure 1), the filtering curve of a filter Q(R) having a cut-off frequency Rmax of (2a) and may have a ~orm as indicated in Figure 3 by a straight line 31.
In Figure 3~ the spatial frequency is plotted on the abscissa and the amplitude o~the (convolution) filter 25 Q(R) is plotted on -~he ordinate. The example shGwn in Figure 3 o~ a ~requency response curve 31 (cut-off frequency (2a) ) o~ a filtering action of the calcula-ting device 16 according to the prior art is described, for example, in g'Indian Journal of Pure and Applied Physics", ~ol.9, November 1971, pp. 997-1003. The curves 31 and 33 sho1~n in Figure 3 are parts of periodical func-tions resulting ~rom a discreet Fourier trans~ormation. These functions be described more fully hereinafter. The filtering to be effected should be tuned -to the sampling frequency and :is cle-te~rrnined by the d:istance a be-tween -the measuring pa-ths and is inversely propor-tional thereto. I-t should be appre-cia-ted that -thereby a:Lso the resolu-tion o~ -the irnage -to be recons-tr-uc-ted ofan objec-t 7 is defined.
-~ ~%~s~
PHN.10,346 9 13.4.1983 In order to increase -the resolution, it has al-ready been suggested -to arrange the detector row L~
asymmetrically to the central ray 30 (Figure 2~ of the source 1, while this ray, passing through the central point 9, strikes the detec-tor 5i~ ~ of the detector 5i lying on one side Or -the central ray 30 and the remaining l part of the de-tector 5i on the o-ther side of the ray 30. The pro-posed asymmetrical arrangement of the detector 5i is obtained by rotation through a quarter of the aperture angle ~ ~/4) of a detec-tor 5i' the source 1 being the centre of this rotation. The detector 5 supplies a measurement value measured along a measuring path 30a. After a rotation of the source 1 and the detector row L~ through an angle ~
of 180, the detector 5i supplies a measurement value asso-ciated with -the measuring path 30b. The measuring paths 30a and 30b are parallel and have a relative clistance a/2 (at the area of the centre of rotation 9)0 It should be appre-ciated that from the groups of measurement values (deter-minative in the different source positions ~i and ei ~ 180) subgroups of measuremen-t values can be selected, -the dis-tance between two adjacen-t measuring paths being a.cos ~ /2. According to the aforementioned publications, such a subgroup is allowed to be filtered by a filter Q(R), the response curve 33 of which is indicated by a broken line in Figure 3. The cut-of~ ~requency is in -this case I/a, ;~ which would mean a doubling of the resolution. On the other hand, i a large memory is required to store all the measure-men-t values (these are a-t least 250 x 223 measurement values of the number of detectors is 250 and the number of source positions is i 180 for a rotation of 180 ); ii the filter-ing canno-t be started until all the required measurement values have been stored and selected (dura-tion a few seconds) and iii -the required calculating operations for the filtering are cloublecl and consequently require a longer caLculating timo or a larger calculating capacity.
In Figure 3, the ~requency response curve Q(R) of a til-tering by -the calc1l:La-ting device according -to the :~%~52~
PHN.10,3~6 10 13.L~.1983 invention is indicated by lines 31 and 31'. In the filtering according to -the invention, the measuremen-t values of a sub-group wi-th the same measuring direction are also processecl.
The subgroup of measuring signals to be fil-ter is measured 5 along measuring paths which have a relative dis-tance a = (r.cos~ y). A second subgroup, which ls measured in the opposite direction, is consequently not interleaved wi-th -the first subgroup before -the filterlng. The filtering can thus be started as soon as the source I (Figure 2) has been lO rotated through an angle 0 = ~(apical angle of radiation beam) because then all the measurement values of a firs-t subgroup have already been measured. The first filtered sub-groups are stored until -the associated second subgroups have been measured and filtered, after which the first subgroup 15 and the associated second subgroup are interleaved (the filtered measurement value of a subgroup is in a posi-tion be-tween two measurement values of the other subgro-up). Such a composi-te overall group consequently would also be obtained if the measurement values had been interleaved before the 20 filtering and had been processed by means of a filter, -the response curve of which is indicated in Figure 3 by lines 31 and 31'. This can be seen as follows. ~ group of measure-ment values obtained according to the prior art (rela-tive ; distance is filtered with fil-tering coefficien-ts (group I) 25 fO, f1, f2, --fN~ fN being -the Nyquist frequency and being determined by (2a) (straight line 31 in Figure 3). If the distance between the measurement values shoulcl be 20a, the Nyquist frequency is 1/a (straight line 33~ Figure 3).
If now a first subgroup of measurement values is filtered 30 according to the invention with the coefficients f ' f1' f2' ... fN and if afterwards a subgroup filtered in -the same manner is interleaved therewi-th, the subgroups in fac-t have been fil-tered wi-th -the coefficien-ts f , 0, f1, 0, f2, ~ ... fN, -the Nyquis-t frequency fN being 1/a and the 35coefficients f1 ~ f2~ e-tc. being associated wi-th frequencies which are two -tirnes h:igher -than the frequenc:ies associated wi-th -the coefficien-ts f1, f2 e-tc of -the group I .
~%~5~
PHN.10,346 11 13.4.1983 Alter having been interleaved, the filtered measurement values are backprojected in a manner known . It should be noted -that in -this case the first filtered subgroups of measuring signals should be stored, wllich requires storage space and waiting time. The back-projection of the first two interleaved subgroups can be started as soon as the second subgroup (antiparallel -to the first subgroup) has been composed and filtered. However, the speed at which such a second subgroup is filtered is four times higher than in case the subgroups should have been interleaved before the filtering (twice -the number of measuring data and twice the number of filtering coeffi-cien-ts) The gain to be achieved consists in that the sub-groups (still to be fil-tered are processed more rapidly, which can be effected simultaneously during the back-projection of subgroups of measuring data already filtered beforehand and subsequently interleaved.
However, in principle it is also possible -that each fil-tered subgroup is backprojected without beîng inter-Z0 leavecl with an associated filtered subgroup. Between each pair of filtered measurement values of each subgroup the values "0" should then be interposed. It is clear that in this case the overall calculating time for carrying out the backprojec-tion is doubled.
The ultimately ob-tained information in the image matrix then has been subjected to an overall frequency filtering which is the product of the frequency response curves of the filtering device, of the back-projection device and of the image matrix.
If the filtered measurement values -to be back-projec-ted are subjected to a linear interpolation, in fac-t a convolu-tion of a -triangular func-tion (having a base wid-th a) is carried out on the E`iltered measurement values (with -a distance of a/2). A convolution in the spatial range can 35 a:Lso be considered as a filtering l~i-th a filter T(R) in the E`requency range. The aforemen-tioned -triangular func-tion has a frequency response curve wllich is de-terminecl by T(R) = sinc (~ a.R). In F:igure 4 this curve is indica-ted ~052~9~
PHN.1o~3~l6 12 13.4.1983 by a line ~5, I-t should be appreciated that (linear) inter-polations in -the backprojection oP -the filtered measurement values lead to an essential unavoidable attenuation of the higher spa-tial frequencies.
The Eiltered measurement values are bac~projected onto an image matrix. It should be apprecia-ted that the size of the image elements of which the image matrix is composed is also de-terminative of the maximum spatial frequency -to be imaged. I~ the size of a (square) image element is P, -the frequency response curve of the image matrix is the Fourier transform G(R) of the block "P" is:
G(R) = sinc(~.P.R.). In Figure 4 the frequency response curve 41 of the image ma-trix with a size P of the image elemen-ts is shown, the distance P being assumed to be equal 5 -to the value a. If -the image matrix has an image element size of 2P, this image matrix has a frequency response curve G~R).sinc(-,~.P,R/2) indicated by a broken line l~3.
Such an image ma-trix requires a memory having a four times larger number of memory cells.
If the measurement values of the antiparallel subgroups are interleaved before the filtering (wi-th a cut-off frequency 2/a~ curve 33, Figure 3) and are backprojected af-ter filtering (filter T(R) = sinc (~.a/2oR)) in an image matrix having an image element size 2a (curve 43, G(R) =
25 sinc(l~a.R) 9 (Figure 4), the overall response curve t~ill have a variation as indicated by -the broken line 51a in Figure 5a. The overall filtering behaviour of -the computer tomography- device is de-termined by the product F(R) = Q(R).T(R).G(R) of the frequencyresponse curves of
3 the convolution fil-ter Q(R); the filter T(R) due to the interpolation and -the filter G(R) due to the frequency limit the influence of the image rna-trix.
If -the subgro-ups of measuring signals in -the device according to the inven-tion are filtered (before first being in-terlea-vecl; curves 31 and 3l~, Figure 3), the over-al:L response curve t~ill have a varia-tion as indica-ted by the full line 53a in Figure 5a. It has been found -that for . , , ~5;~
PHN.10,346 13 13.4.1983 frequencies smaller than 0~5/a no loss occurs. However, the loss for -the frequencies between 0.5/a and 1/a is to a high e~tent not essential because these frequencies in themselves only add additional informa-tion to theultimate image and -to a lligh e~tent carry along "noise signals~. In the device according -to the invention~ in which the measurement values are filtered immediately af`ter measuring and by means of an associated filter with a cut-off frequency of 1/a, an image with a high resolu-tion is thus obtained, the noise being suppressed to a large extent, while a saving in calculating time is realized and the wai-ting time from the beginning of the measurement to the beginning of the filtering of the measuring data is shortened considerably (from 2 seconds to 0.5 second)~
If the filtered measurement values are back-projected onto an image matrix having as image element size a, the filtering is determined by G(R) = sinc(7~.a.R) (curve 41, Figure 4). The overall filtering behaviour F(R) '~ of -the convolution device according to the inven-tion is then ~; as indicated by the curve 53b in Figure 5b. The overall filtering behaviour of a device according to the prior art is indicated by the curve 51b~ It can now been seen very clearly that the behaviour of the device according to -the invention with respect to the high frequencies (0.5/a) does not deviate considerably from that of the device according to the prior art.
In the ~bove description of the frequency-limiting properties of computer tomography devices~ the dis-tance a between the various measuring pa-ths has been -taken into accoun-t. However, the width of the beam of ~-ray radiation has not been tak0n into accoun-t. If it is assumed that the width of such a beam is also a along a measuring pa-th at -the area of -the centre of ro-tation 9 (and wi-th respect to -the intensity has~ viewed at righ-t angles -to -the dLrection of radiation~ a rectangular variation) 9 such a beam will have a -~requency (R)-lirni-ting behaviour which is indicated by B(R) = sinc(/L.a.R). The curves 51a~b and 53a,b 5;~
PIIN.10.346 14 ~3.4.1983 from Figures 5a and 5b should be multipliecl once more by the function B(R) so that the difference between the curves 51a and 53a and between 51b and 53b becomes smaller once more for the frequencies between 0.5/a and 1/a.
It should be noted that in the example described above the so-called "Ramp" filter was used for fil-tering the subgroups. However, the invention is not limited to this filter and can be used equally effectively in computer tomography devices in which the high-frequency con-tent of lO the measuring signals is already at-tenuated (this is the case in C.T. devices in which the so-called "Shepp" filter is utili~ed), see, for example, I.E.E.E. Trans. Nucl.Science, NS ~1, 21-43~ 1971. In such devices, the overall frequency response curves for high frequencies will in fact become 15 located closer to each other.
.
':
:' .,
If -the subgro-ups of measuring signals in -the device according to the inven-tion are filtered (before first being in-terlea-vecl; curves 31 and 3l~, Figure 3), the over-al:L response curve t~ill have a varia-tion as indica-ted by the full line 53a in Figure 5a. It has been found -that for . , , ~5;~
PHN.10,346 13 13.4.1983 frequencies smaller than 0~5/a no loss occurs. However, the loss for -the frequencies between 0.5/a and 1/a is to a high e~tent not essential because these frequencies in themselves only add additional informa-tion to theultimate image and -to a lligh e~tent carry along "noise signals~. In the device according -to the invention~ in which the measurement values are filtered immediately af`ter measuring and by means of an associated filter with a cut-off frequency of 1/a, an image with a high resolu-tion is thus obtained, the noise being suppressed to a large extent, while a saving in calculating time is realized and the wai-ting time from the beginning of the measurement to the beginning of the filtering of the measuring data is shortened considerably (from 2 seconds to 0.5 second)~
If the filtered measurement values are back-projected onto an image matrix having as image element size a, the filtering is determined by G(R) = sinc(7~.a.R) (curve 41, Figure 4). The overall filtering behaviour F(R) '~ of -the convolution device according to the inven-tion is then ~; as indicated by the curve 53b in Figure 5b. The overall filtering behaviour of a device according to the prior art is indicated by the curve 51b~ It can now been seen very clearly that the behaviour of the device according to -the invention with respect to the high frequencies (0.5/a) does not deviate considerably from that of the device according to the prior art.
In the ~bove description of the frequency-limiting properties of computer tomography devices~ the dis-tance a between the various measuring pa-ths has been -taken into accoun-t. However, the width of the beam of ~-ray radiation has not been tak0n into accoun-t. If it is assumed that the width of such a beam is also a along a measuring pa-th at -the area of -the centre of ro-tation 9 (and wi-th respect to -the intensity has~ viewed at righ-t angles -to -the dLrection of radiation~ a rectangular variation) 9 such a beam will have a -~requency (R)-lirni-ting behaviour which is indicated by B(R) = sinc(/L.a.R). The curves 51a~b and 53a,b 5;~
PIIN.10.346 14 ~3.4.1983 from Figures 5a and 5b should be multipliecl once more by the function B(R) so that the difference between the curves 51a and 53a and between 51b and 53b becomes smaller once more for the frequencies between 0.5/a and 1/a.
It should be noted that in the example described above the so-called "Ramp" filter was used for fil-tering the subgroups. However, the invention is not limited to this filter and can be used equally effectively in computer tomography devices in which the high-frequency con-tent of lO the measuring signals is already at-tenuated (this is the case in C.T. devices in which the so-called "Shepp" filter is utili~ed), see, for example, I.E.E.E. Trans. Nucl.Science, NS ~1, 21-43~ 1971. In such devices, the overall frequency response curves for high frequencies will in fact become 15 located closer to each other.
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Claims (3)
1. A method of determining a radiation attenuation distribution in a plane of a body, in which the body is irradiated from a multitude of directions passing through a central point and distributed over 360° with a flat fan-shaped beam of penetrating radiation diverging from one point for determining a group of measuring data for each measuring direction, which are measured along a number of measuring paths located in the plane of the body and which are a measure for the attentation of the radiation in the body occurring along the number of diverging measuring paths, an imaginary line passing through a central point in each direction enclosing a quarter of an angle enclosed by two adjacent measuring paths with a central measuring path, while a measuring path has a maximum width a which is measured along a line which is at right angles to the measuring path and passes through the central point, after which from the groups of measuring data subgroups are de-termined which are measured along (imaginary) measuring paths with the same measuring direction, whereupon each subgroup is filtered either through a convolution calculation or through a Fourier transformation, a filtering and a Fourier backtransformation and is backprojected onto an image matrix, characterized in that from the groups of measuring data for each measuring direction two subgroups are selected, measuring data of the first subgroup being measured along measuring paths which are antiparallel to measuring paths along which the measuring data of the second subgroup are determined, while in each subgroup the dis-tance between two measuring paths is at most a and larger than ? a and the filtering of each subgroup is carried out by means of a filtering device the frequency response curve of which has a maximum for the frequency (2a)-1 and zero points for the frequencies O and 1/a, whereupon each first subgroup of filtered measuring data is interleaved with the measuring data of the associated second subgroup and the interleaved subgroups of measuring data are backprojected, an interpolation distance between the measuring data being a/2.
2. A computer tomography device for determining a radiation attenuation distribution in a plane of a body, which device comprises:
- at least one source for producing a flat fan-shaped beam of penetrating radiation for irra-diating the body along a number of measuring paths diverging from the source and located in the plane from a multitude of directions passing through a central point and distributed regularly over 360°;
- a series of detectors for detecting radiation passed through the body along the measuring paths for supplying for each direction a group of measuring data which are a measure for the attenuation of the radiation occurring in the body along the number of diverging measuring paths, radiation emitted by the source and passing through the central point striking a detector at the centre of a row spanned by the fan-shaped beam halfway between the centre and the edge thereof, while a measuring path has a maximum width a which has been measured along a line which is at right angles to the measuring path an passes through the centre of the central point;
- a calculating device with a memory for storing measuring data and for determining subgroups of measuring data which are measured along (imaginary) measuring paths with the same direction;
- a calculating device with a filtering device for carrying out a convolution or a Fourier transformation, a frequency filtering and a Fourier backtransformation of each subgroup of measuring data;
- a calculating device with a backprojection device for distributing and adding values of each subgroup of filtered measuring data respectively over and to a matrix of memory cells of the memory which constitute an image matrix;
- a display device for displaying the content of the image matrix, characterized in that the calculating device determines for each measuring direction two subgroups of measuring data from the groups of measuring data measured over 360°, the measuring data of one subgroup being measured in a direction opposite to that in which the measuring data of the other subgroup are measured, while the distance between two meas-uring paths associated with two adjacent measuring data in a subgroup is at most a and larger than a/2, in that the filtering device has a frequency response curve with a maximum for the frequency (2a)-1 and zero points for the frequencies 0 and 1/a, and in that the backprojection device distributes each pair of interleaved subgroups of filtered values with an interpolation distance a/2 over the image matrix and adds these subgroups to this image matrix, the number of memory cells of which is larger than the number of detectors spanned by the beam of diverging radiation.
- at least one source for producing a flat fan-shaped beam of penetrating radiation for irra-diating the body along a number of measuring paths diverging from the source and located in the plane from a multitude of directions passing through a central point and distributed regularly over 360°;
- a series of detectors for detecting radiation passed through the body along the measuring paths for supplying for each direction a group of measuring data which are a measure for the attenuation of the radiation occurring in the body along the number of diverging measuring paths, radiation emitted by the source and passing through the central point striking a detector at the centre of a row spanned by the fan-shaped beam halfway between the centre and the edge thereof, while a measuring path has a maximum width a which has been measured along a line which is at right angles to the measuring path an passes through the centre of the central point;
- a calculating device with a memory for storing measuring data and for determining subgroups of measuring data which are measured along (imaginary) measuring paths with the same direction;
- a calculating device with a filtering device for carrying out a convolution or a Fourier transformation, a frequency filtering and a Fourier backtransformation of each subgroup of measuring data;
- a calculating device with a backprojection device for distributing and adding values of each subgroup of filtered measuring data respectively over and to a matrix of memory cells of the memory which constitute an image matrix;
- a display device for displaying the content of the image matrix, characterized in that the calculating device determines for each measuring direction two subgroups of measuring data from the groups of measuring data measured over 360°, the measuring data of one subgroup being measured in a direction opposite to that in which the measuring data of the other subgroup are measured, while the distance between two meas-uring paths associated with two adjacent measuring data in a subgroup is at most a and larger than a/2, in that the filtering device has a frequency response curve with a maximum for the frequency (2a)-1 and zero points for the frequencies 0 and 1/a, and in that the backprojection device distributes each pair of interleaved subgroups of filtered values with an interpolation distance a/2 over the image matrix and adds these subgroups to this image matrix, the number of memory cells of which is larger than the number of detectors spanned by the beam of diverging radiation.
3. A computer tomography device as claimed in Claim 2, characterized in that the number of memory cells is about four times the square of the number of detectors spanned by the fan-shaped beam.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| NL8201942 | 1982-05-12 | ||
| NL8201942A NL8201942A (en) | 1982-05-12 | 1982-05-12 | METHOD AND COMPUTER TOMOGRAPHY DEVICE FOR DETERMINING A TOMOGRAPHY IMAGE WITH INCREASED RESOLUTION. |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1205214A true CA1205214A (en) | 1986-05-27 |
Family
ID=19839718
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000427539A Expired CA1205214A (en) | 1982-05-12 | 1983-05-05 | Method and computer tomography device for determining a tomographic image with elevated resolution |
Country Status (7)
| Country | Link |
|---|---|
| US (1) | US4555760A (en) |
| EP (1) | EP0094124B1 (en) |
| JP (1) | JPS58206729A (en) |
| CA (1) | CA1205214A (en) |
| DE (1) | DE3365095D1 (en) |
| IL (1) | IL68633A (en) |
| NL (1) | NL8201942A (en) |
Families Citing this family (15)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4637040A (en) * | 1983-07-28 | 1987-01-13 | Elscint, Ltd. | Plural source computerized tomography device with improved resolution |
| JPS6085357A (en) * | 1983-10-17 | 1985-05-14 | Toshiba Corp | Nuclear magnetic resonator video apparatus |
| FR2553898B1 (en) * | 1983-10-25 | 1986-03-21 | Thomson Csf | METHOD OF ACQUISITION AND RECONSTRUCTION OF IMAGE BY TOMODENSITOMETRY, AND TOMODENSITOMETER IMPLEMENTING THIS METHOD |
| FR2562371A1 (en) * | 1984-03-30 | 1985-10-04 | Thomson Cgr | METHOD FOR RECONSTRUCTING HIGH RESOLUTION IMAGE BY TOMODENSITOMETRY |
| US4729100A (en) * | 1984-08-28 | 1988-03-01 | Kabushiki Kaisha Toshiba | CT System which convolutes projection data with a frequency varying filter function |
| JPH0750501B2 (en) * | 1984-09-19 | 1995-05-31 | 株式会社日立メディコ | X-ray CT system |
| JPS6198239A (en) * | 1984-10-18 | 1986-05-16 | 株式会社日立メディコ | X-ray ct apparatus |
| GB2181330B (en) * | 1985-09-26 | 1990-05-09 | Toshiba Kk | X-ray inspection apparatus |
| JPH0799539B2 (en) * | 1985-09-30 | 1995-10-25 | ジーイー横河メディカルシステム株式会社 | Radiation tomography equipment |
| US5079697A (en) * | 1989-05-01 | 1992-01-07 | The General Hospital Corporation | Distortion reduction in projection imaging by manipulation of fourier transform of projection sample |
| JP3653992B2 (en) * | 1998-06-26 | 2005-06-02 | 株式会社日立製作所 | Computer tomography apparatus and computer tomography method |
| WO2006058124A1 (en) * | 2004-11-24 | 2006-06-01 | Wisconsin Alumni Research Foundation | Fan-beam and cone-beam image reconstruction using filtered backprojection of differentiated projection data |
| US7672421B2 (en) * | 2005-10-12 | 2010-03-02 | Siemens Medical Solutions Usa, Inc. | Reduction of streak artifacts in low dose CT imaging through multi image compounding |
| US8116426B2 (en) * | 2008-11-11 | 2012-02-14 | Kabushiki Kaisha Toshiba | Computed tomography device and method using circular-pixel position-adaptive interpolation |
| US9224216B2 (en) * | 2013-07-31 | 2015-12-29 | Kabushiki Kaisha Toshiba | High density forward projector for spatial resolution improvement for medical imaging systems including computed tomography |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4066903A (en) * | 1974-07-20 | 1978-01-03 | Emi Limited | Radiology |
| US4398251A (en) * | 1974-12-19 | 1983-08-09 | Emi Limited | Radiography |
| US4051379A (en) * | 1975-11-28 | 1977-09-27 | Artronix, Inc. | Axial tomographic apparatus and detector |
| US4088887A (en) * | 1975-12-10 | 1978-05-09 | Emi Limited | Radiography method comprising determination of corrected absorption values for members of sets of mutually inclined beam paths |
| US4365339A (en) * | 1975-12-23 | 1982-12-21 | General Electric Company | Tomographic apparatus and method for reconstructing planar slices from non-absorbed and non-scattered radiation |
| US4326252A (en) * | 1976-11-29 | 1982-04-20 | Hitachi Medical Corporation | Method of reconstructing cross-section image |
| NL7902015A (en) * | 1979-03-14 | 1980-09-16 | Philips Nv | METHOD AND APPARATUS FOR DETERMINING A RADIATION ABSORPTION DISTRIBUTION IN PART OF A BODY. |
| NL7908545A (en) * | 1979-11-23 | 1981-06-16 | Philips Nv | DEVICE FOR DETERMINING A RADIATION ABSORPTION DISTRIBUTION IN A SURFACE OF A BODY. |
| JPS56136529A (en) * | 1980-03-28 | 1981-10-24 | Tokyo Shibaura Electric Co | Apparatus for reconstituting image |
-
1982
- 1982-05-12 NL NL8201942A patent/NL8201942A/en not_active Application Discontinuation
-
1983
- 1983-05-03 EP EP83200630A patent/EP0094124B1/en not_active Expired
- 1983-05-03 DE DE8383200630T patent/DE3365095D1/en not_active Expired
- 1983-05-04 US US06/491,516 patent/US4555760A/en not_active Expired - Fee Related
- 1983-05-05 CA CA000427539A patent/CA1205214A/en not_active Expired
- 1983-05-09 IL IL68633A patent/IL68633A/en unknown
- 1983-05-11 JP JP58081062A patent/JPS58206729A/en active Granted
Also Published As
| Publication number | Publication date |
|---|---|
| DE3365095D1 (en) | 1986-09-11 |
| JPH0470015B2 (en) | 1992-11-09 |
| IL68633A (en) | 1987-03-31 |
| EP0094124A1 (en) | 1983-11-16 |
| JPS58206729A (en) | 1983-12-02 |
| NL8201942A (en) | 1983-12-01 |
| US4555760A (en) | 1985-11-26 |
| EP0094124B1 (en) | 1986-08-06 |
| IL68633A0 (en) | 1983-09-30 |
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