WO1989009973A1

WO1989009973A1 - Backprojection apparatus and method

Info

Publication number: WO1989009973A1
Application number: PCT/US1988/004352
Authority: WO
Inventors: Leopold Neumann
Original assignee: Analogic Corporation
Priority date: 1988-04-13
Filing date: 1988-12-07
Publication date: 1989-10-19
Also published as: CN1037421A; EP0368941A4; EP0368941A1; JPH02503840A

Abstract

The present invention relates to the process of backprojecting image data from a plurality of sets of projection data produced from different angular positions around a center of rotation within an imaging plane. In the interest of reducing the complexity of the mathematical process the present invention provides circuitry (32) for backprojecting each set of projection data into pixel values for a polar coordinate image, and for summing the corresponding pixel values backprojected from substantially all of the sets of projection data. This invention has particular use in reducing the cost and complexity of CAT scanners.

Description

BAC PROJECTION APPARATUS AND METHOD

BACKGROUND OF THE INVENTION Field of the Invention

The present invention generally relates to electronic image processing backprojectors used for mathematically reconstructing images from multiple sets of projection data taken at different angles around a center of roatation within an imaging plane, such as those produced by CAT scan apparatuses, and in particular, to such backprojection apparatuses which process the image data during scanning to produce an image practically instantaneously with the conclusion of the scanning operation. Statement of the Prior Art

Image reconstruction from scan data and the electronic circuitry for performing such have been under study and developement for many years. In various forms, data from one or more scans are mathematically compiled to produce a representative image. In the area of CAT scanning (computerized axial tomography), one approach includes an x-ray source and an array of detectors located on opposite sides of a patient or other object and rotated around that patient or other object, and within an imaging plane, while the detector outputs are measured, either instantaneously or over time, at different angular positions. This measured data is then electronically conditioned, sampled, corrected, convolved and interpolated to produce projection data representing the x-ray density of the patient or other object, as projected on the detectors. One set of projection data is produced for each view measured by the detector array. In a typical CAT scan apparatus one or more projection views of the patient is taken for each degree of rotation, for a total of 360 or more views or sets of projection data per scan. These multiple sets of projection data are then compiled in a process known as backprojection to produce a single image. In the earlier days of CAT scanning, backprojection was accomplished with a large co puter in a time frame well after the scanning was performed. Over time, the delay in this processing was greatly reduced up to and including the invention of "instant imaging" CAT scanning as described in U.S. Patent No. 4,135,247 of Bernard M. Gordon, et al. This patent includes a rather detailed explanation of the entire CAT scanning process as well as the backprojection process.

The prior process described in the patent produces image data during the scanning process for each complete set of projection data. First, orthogonal coordinate addresses are generated for each pixel of the image to be produced. By calculation, these orthogonal coordinate addresses are converted into orthogonal coordinates for each set of projection data as they are produced in the scanning apparatus. A lookup and interpolation process is then used to find locator and weighting data for each pixel. The locator data determines which data point of the processed projection data is to be multiplied by the corresponding weighting data. The product is then added to the contents of a separate image memory which accumulates a sum for each pixel. Because this process is performed for each complete set of projection data and is ongoing during the scan process, it results in formation of the image during the scan and a completed image shortly after the conclusion of the scan, hence the term "instant imaging."

In the interest of furthering the art of backprojection, the speed, equipment cost, and reliability of this process could be improved by simplification and reduction of the complexity of the numerous calculation steps used. SUMMARY OF THE INVENTION

Accordingly, a backprojection apparatus and method is provided which significantly simplifies the required calculation. The present invention provides image data for a single image from a plurality of sets of projection data produced from different angular positions around a center of rotation within an imaging plane, comprising means for backprojecting each set of projection data into pixel values for a polar coordinate image, and for summing the corresponding pixel values backprojected from substantially all of the sets of projection data. In one embodiment, the means for backprojecting and for summing includes a plurality of processor means each adapted to simultaneously backproject a separate set of projection data into polar coordinate pixel values. Included are addressable memory means for storing corresponding locator and weighting data for each polar image pixel location, and means for coupling identical locator and weighting data addressed from the memory means to each of the plurality of processor means. Also included are second addressable memory means for storing polar image pixel values, with each processor means including third addressable memory means for storing at least one set of projection data, means for addressing the third memory means with the locator data^' from the first said memory means, and multiplier means for producing the product of projection data from the third memory means and corresponding weighting data from the first said memory means. The method of the present invention provides for backprojecting image data for a single image from a plurality of sets of projection data produced from different angular positions around a center of rotation within an imaging plane, comprising the steps of backprojecting each set of projection data into pixel values for a polar coordinate image, and summing the corresponding pixel values backprojected from substantially all of the sets of projection data.

BRIEF DESCRIPTION OF THE DRAWINGS The present invention is illustratively described below in reference to the appended drawings of which:

Fig. 1 is a representational side view of a CAT scan apparatus;

Fig. 2 is a block diagram of the data processing circuitry employed in accordance with one embodiment of the present invention;

Fig. 3 is a block diagram of a backprojector constructed in accordance with one embodiment of the present invention; Fig. 4 is a block diagram of a backprojector constructed in accordance with another embodiment of the present invention;

Fig. 5 is a detail block diagram of a portion of the circuitry of Fig. 3.

Fig. 6 is an example of a polar coordinate image pixel arrangementproduced by the present invention; and

Fig. 7 is a table showing the flow of image pixel vvalues from the arrangement of Fig. 5 as processed throughthe described embodiment of the present invention. DETAILED DESCRIPTION OF THE DRAWINGS Fig. 1 represents a CAT scan apparatus generally including an x-ray source 10 which produces a fan beam 12 of x-rays. X-rays 12 impinge upon an array 14 of x-ray detectors. The x-ray source 10 and array 14 are affixed to a rotatable ring 16 which mounts the array 14 by its ends 17. The ring 16 is rotatably mounted within a stationary ring 18 and has a center of rotation at point 20. The boundaries of the fan beam 12 rotationally define an imaging area 22 within which a patient or other object may be located for x-ray imaging. The image produced represents a cross-section of the patient at an imaging plane within which the x-ray source_. 10 and detector array 14 rotate.

In producing the projection data, the outputs of the detectors are measured either instantaneously or for predetermined periods of time at many different angular positions of the rotatable ring 16. The outputs of the detectors represent the x-ray density of an object being x-rayed as projected against the detector array 14 by the source 10 and are therefore termed projection data.

Output signals from the detector array 14 are coupled to the electronic circuitry represented by the block diagram of Fig. 2. That circuitry provides signal conditioning, data acquisition, data correction, convolution, interpolation, image backpro ection, ring filtering, scan conversion, and display of a completed display image. Fig. 2 shows the detectors 14, signal conditioning circuitry 24, an analog to digital (A/D) converter 26, a data corrector 28, a data convolver/interpolator 30, a backprojector 32, a ring filter 33, a scan converter 34, and a display means 36. The signal conditioning circuitry 24 and the A/D converter 26 are typically mounted with the detectors 14 on the rotatable ring 16. This enables very short connections between this circuitry and minimizes the amount of signal loss, noise, and. other interference which might cause inaccuracies in the measured data. A/D converter 26 may be a logarithmic converter for providing data in the proper form for the reconstruction process. The digitized data representing the detector outputs is then transmitted by some form of electronic link 27 to the data corrector 28. The link 27 is typically effected without direct physical connection to enable free rotation of the apparatus of Fig. 1 and for reducing any interference which might be interjected with the data. Data corrector 28 corrects the digital data for various anomalies known in the x-ray art, such as beam hardening, detector spacing errors, nonlinearity, sensitivity, gain and offset variations, and the like. The scan projection data is then coupled to the convolver 30 which digitally filters the projection data.

The components of Fig. 2 discussed thus far are intended to be essentially similar to those components described in the aforesaid U.S. Patent No. 4,135,247. These functions may be performed by any suitable means including those described in the aforesaid patent.

The convolved and interpolated projection data is then coupled to the backprojector 32 which backprojects the separate sets into a single set of image data based upon a polar coordinate arrangement. This arrangement consists of a number of concentric rings each of which contains a predetermined number of pixels, which pixels are radially aligned. Backprojection into a polar coordinate image allows the use of either one or a small number of sets of locator and weighting data for backprojecting many sets of projection data into a single image. The prior art requires so much ore locator and weighting data that the data must be calculated, whereas the locator and weighting data for backprojecting a single image with the present invention may be stored in a memory and simply addressed sequentially. Thus, the present invention significantly simplifies the process and further allows simultaneous conversion of several sets of projection data. Identical locator and weighting data may be used because the polar coordinate system of the backprojected image may be set up to have an identical mathematical .relationship with each of the views of projection data. The only difference between the polar coordinates seen from each view is a difference of rotation of the pixels. The identical mathematical relationship between the projection data and the polar pixels is achieved by correlation between the number of pixels in each concentric ring and the number of views of projection data. This is discussed in greater detail in reference to Fig. 6.

It should also be noted that the resolution provided by a polar coordinate image increases in the direction of the center of the image. This is particularly well suited to CAT scanning as the center of the images so produced typically contain the most important and complex structures.

As the sets of projection data are received by the backprojector, they are stored in a random access memory which is then addressed in accordance with the backpro ection process. The resulting polar coordinate image data is stored in memory within the backprojector and the contribution of each succeeding set of projection data is likewise backprojected and added to the corresponding polar coordinate pixel values.

Once all of the sets of projection data are backprojected into the single polar coordinate image, that image is coupled to an optional ring filter 33. Because the backprojected image is in the polar coordinate form it is particularly well suited to the filtering of ring artifacts. Rings are generally caused when the projection data corresponding to a single detector is in error for any one of a number of reasons. Because each detector is associated with adjacent data in the backprojected image, in this case concentric rings, a consistent error associated with a detector is more readily visible. The error appears as a ring on the image. The polar coordinate form of the present invention is particularly well suited to the detection and filtering of rings. Any suitable method of ring filtering may be used. For example, the data may first be high pass filtered in the radial direction which would cause anomalies to be highlighted. Subsequent low or band pass filtering in the concentric ring direction would allow identification of rings and their removal. The polar coordinate image data is in excellent form for each of these processes. The rings and radians of the polar image may be stored in memory as respective rows and columns and addressed accordingly.

The ring filtered polar coordinate image data or the unfiltered backprojection data is next coupled to the scan converter 34 which performs a routine scan conversion process resulting in an orthogonal coordinate image which may then be displayed by the display means 36. The scan conversion process may take any suitable form such as selecting the closest corresponding polar coordinate pixel, selecting the closest from a more densely pixelled interpolated polar image, or interpolating the orthogonal pixels from either the backprojected polar pixels or the interpolated polar pixels. As shown in Fig. 3, the backprojector 32 includes an address generator 40, a lookup table 42, a multiplicity of processor units or means 44, and a polar image memory 46. The lookup table 42 includes locator and weighting data for backprojecting the scan projection data into polar image pixel values. This information is caused to be read out of the lookup table 42 by the address generator 40, and identical data is coupled to each of the processor means 44. Each processor unit 44 contains memory means therein for storing a separate set of projection data which each unit uses for complementing polar image pixel values stored in raemory 46. The projection data is inputed to each unit 44 via a port 48.

As the address generator 40 clocks locating and weighting data from the lookup table 42, it simultaneously addresses corresponding polar image pixel addresses in the polar image memory 46. The pixel values stored therein are correspondingly coupled through the processor means 44 by means of serial connections where the data is complemented by contributions from each set of projection data. The address sequence of the address generator 40 may be predetermined which allows the lookup table 42 to be implemented as a differential lookup table. To accomplish this, lookup table 42 consists of an output accumulating-sum device 41, 43 for each of the locator and weighting data, respectively, and a sequentially addressed memory 45 which stores only the difference values for determining the locator and weighting factors. Use of a differential table requires less storage capacity because it is only the least significant bits which are needed for each step. The sequential addressing also allows the use of a simpler form of memory, such as a recirculationg shift register. This technique is especially suited to the present invention as explained in reference to Fig. 6.

Fig. 4 shows an alternate embodiment of the backprojector 32. In this embodiment reference numerals which are identical to those of Fig. 3 refer to similar devices which function in a similar manner to those in Fig 3 and only the differences are described herein. The most substantial difference of Fig. 4 is the inclusion of the summing means 47 which has a pair of inputs coupled to the output of processor D and the data output of memory 46, respectively. Summing means 47 also has an output coupled to the data input of memory 47. In operation, pixel data stored in memory 46 is not coupled through the processors, but instead is simply updated in the summing means 47 with the contributions calculated and accumulated in the processors. The updated values are then restored in memory 46. As shown in Fig. 5, each of the processor means 44 generally includes a memory 50, a multiplier 52, a delay register 51, a summation means 54, and a delay register 56. Data for one projection set is stored in memory 50 through an 5 input port 48. This data is addressed by means of the locator data coupled from the lookup table 42 over a bus 60. Bus 60 is part of a larger bus 61 from lookup table 42. The projection data so addressed is outputted through a port 62 to an input of the multiplier 52. Simultaneously, 10 corresponding weighting data is coupled from the lookup table 42 through a bus 64 to the other input of multiplier 52. The data at these inputs is multiplied and the product is coupled to delay register 51. Register 51 includes a pipelined register 53 and a multiplexor 55 and is used for the 15 temporary storage of cetain pixel values as explained below. . The output of multiplexor 55 is coupled to summation circuit 54. Simultaneously, image pixel data corresponding to the same polar coordinate is inputted via a data bus 66 and the contribution just calculated from the projection data _.υ is added in summation circuit 54 to this previously calculated pixel value. The sum of this pixel value is then coupled through the delay register 56 and on to further processing means 44 or back to the polar image memory 46. Delay register 56 likewise consists of a multiplexor 57 and a - ^' => pipelined shift register 59 and is used to provide a temprary delay to certain pixel values as explained below. The amount of the delay from register 56 depends upon the ratio of the number of sets of projection data to the number of pixels in the polar coordinate image as explained below. 30 Figs. 6 and 7 demonstrate the generation and flow of image data through the embodiment of the present invention described above. Fig. 6 displays a polar coordinate image having pixals numbered 00 through 4F. This representaiton is an extremely simplified form of a polar coordinate image 5 which might be produced by the present invention. The simplification is for purposes of clarity here. The polar coordinate image of Fig. 6 is arranged in a series of 5 concentric circles which are identified by the left digit of each pixel number, hence, 0 through 4. Each concentric circle contains 16 separate pixels which are numbered 0 through F in hex. This pixel identification is represented by the right digit of each pixel number. This pixel number may also be said to represent and identify the various radial sections of the image.

An arrow in the upper right hand corner shows the counter clockwise rotational direction of the CAT scan gantry with respect to the polar coordinate system which results in the series of projection data views VI through V8 which are positionally labelled in Fig. 6. Thus the x-ray apparatus collects a single set of projection data when the x-ray source 10 is located at each of the indicated viewpoints V1-V8. Of course, the rotation continues and a set of projection data is taken for each of the 16 radial sections of the system. Identification of the first 8 views is all that is necessary for the purpose of explaining the operation of this embodiment. Of particular note with respect to Fig. 6 is the geometric relationship between the views V1-V8 and the pixel locations. The same locator and weighting data which is used to calculate pixel 00 from view VI is used to calculate OF from V2, 0E from V3 and 0D from V4. This allows simultaneous calculation of these four values, and similarly related values, in the four processors of Fig. 3, while they are all using the same locator and weighting functions.

With simultaneous reference to Fig. 3, 5, 6 and 7, the four sets of projection data V1-V4 are stored in the memory 50 of a separate processsor unit A through D, respectively, in Fig. 3. The address generator 40 produces addresses which are simultaneously delivered to the lookup table 42 and the polar image memory 46. Thus, locator and waiting data are delivered from the look up table 42 in correspondence with the polar image memory pixel being addressed in memory 46.

The flow of the pixel values through the processor means A through D and the memory 46 is shown in Fig. 7. The sequential processing steps are numbered on the first line from left to right. The pixel values being inputted from memory 46 are identified on the second line labelled DATA IN and correspond to the polar coordinate system shown in Fig. 6. The separate projection data sets and the corresponding processors A through D in which they are stored are identified in the left column. The corresponding pixel values which are calculated from each respective projection data set during each sequential processing step are shown in sequence to the right of their respective processors A through D. An underlined pixel number (_0JD) indicates data which is stored in the shift register 53 of its respective processor. The bottom line of Fig. 7 corresponds to data which is stored into the memory 46. At the first step in the calculation process, each processor 44 receives weighting data which corresponds to pixel 00 for view VI, OF for view V2, 0E for view V3, and 0D for view V4. Any value for pixel 00 stored in memory 46 is delivered to the data input of processor A. During the first step, each processor A through D calculates the contribution of its respective projection data set to the respective pixel 00, OF, 0E, and 0D. At the conclusion of the multiplication the product from the multiplier of each processor B, C, and D is stored in the shift register 53 of its respective processor and the product from processor A is summed with any residual value from memory 46 and coupled to the input of adder 54 of processor B.

For the second processing step new locator data causes any value stored in memory 46 for pixel 01 to be coupled to processor A. Processors A through D calaculate contributory products for each of the pixels 01, 00, OF and 0E, respectively. At the conclusion of the multiplication, processors C and D store their respective products in their respective shift registers 53 and processors A and B sum their products with any previouly accumulated sums transfered thereto and transfer the summed pixel values for pixels 00 and 01 to processors C and B, respectively. For processing step 3, processor A receives any value for pixel 02, and contributions to the values of pixels 02, 01, 00 and OF are respectively calculated by the processors A through D. At the conclusion of the multiplication of step 3, processors A through C sum their products with any previously calculated values and transfer their accumlated sums into the next sequential processor and the value for pixel OF in processor D is stored in shift register 53 of processor D. At the conclusion of step 3 the respective shift registers 53 hold values for pixels OF, 0E, and 0D in processor A; OF and 0E in processor B; and OF in processor C. These values are left in this storage until they are needed later. During processing step 4, values are calculated for pixels 03, 02, 01 and 00 by the respective processors A through D. At the conclusion the accumulated value for pixel 00 is stored in memory 46 and the accumulated values for pixels 01,02, and 03 are transferred to the next suceeding processor. Likewise, during subsequent processing steps 5 through 16 the accumulated sums for pixels 01 through 0C are stored directly into memory 46 after being sequenced through each of the processors.

At the beginning of processing step 17, locator and weighting data for pixels 10, IF, IE. and ID and delivered to the processors A through D, respectively. During step 17, the multiplier of processor D produces a product for ID which is stored in its shift register 53 causing the previously stored contribution to 0D to be transferred to the adder 54. There it is added to the accumulated contributions to 0D from views V1-V3 calculated in steps 14-16. At the conclusion of step 17, the new value for 0D is stored in memory 46. Likewise during step 17, processor C stores the product for pixel IE while summing the contibutions for pixel 0E and processor A stores the product for pixel IF while summing the contributions for pixel OF. Likewise during step 18, processor D stores the product for pixel IE in its shift register 53 while summing contributions for pixel 0E and causing that sum to be stored in memory 46. Meanwhile, processor C is storing a product for pixel IF while summing contributions for pixel OF. Lastly, during step 19, processor D stores the product for pixel IF in its shift register 53 while summing contributions for pixel OF and causing its storage in memory 46.

At the conclusion of step 80 of Fig. 7, partially summed contributory values for the pixels 4D, 4E, and 4F are stored in registers 53 and adders 54 of the processors A through D. These values are summmed through the adders 54 and stored in memory 46 in three extra steps 81-83 in the same manner as pixels ID, IE, and IF of steps 17-19 and other corresponding pixels.

During the porcessing of the first four sets of projection data V1-V4, a second set of four sequential views V5-V8, or sets of projection data are being loaded into the memories of each of the processors 50 so that processing may continue uninterrupted.

The backprojector of Fig. 4 may be used in substantially the same manner as the method described for Fig. 3. The only major difference arises in the line of Fig. 7 labelled DATA IN. In Fig. 4 accumulated pixel values are not recirculated through the processors they are only updated by the summing means 47 in correspondence with contibutions coupled from processor D. Thus the data for Fig. 7 in reference to Fig. 4 would remain the same but for the deletion of the DATA IN line. Although this approach negates the necessity for the adding means 54 in processor A, it may be preferred for the addressing requirments of memory 46.

The present embodiment of the invention may also be used when the number of pixels in each concentric ring of the polar image is an interger multiple of the number of views. By way of example assume that only the odd numbered views VI, V3, V5, and V7 are available for calculations. These views would be loaded into processors A-D, respectively. Simultaneous products would be calculated for the pixels 00 of VI, 0E for V3, 0C of V5 and 0A of V7. The products for 0E, 0C, and 0A would be stored in the shift registers 53 of their respective processors and the accumulated value for 00 5 would be stored in the shift register 59 of processor A. There the value is stored for one processing step. During the second step products would be calculated for the pixels

01 of VI, OF of V3, 0D of V5 and 0B of V7. Products for OF, 0D, and 0B would be stored in respective shift registers 53,

10 while an accumulated sum for 01 would be stored in the shift register 59 of processor A, causing the previously stored value for 00 to be transferred to processor B.

During the third step products would be calculated for

02 of VI, 00 of V3, 0E of V5 and 0C of V7. The product for 1500 produced in processor B would be added to the previous sum transferred for processor A. Thusly, the shift registers 59 are used as an interim delay for pixel values not being calculated during any given processing step. Where there are twice as many pixels in each concentric ring of the polar

20 image as there are sets of projection data there is one unused pixel value residing in each of the shift registers 59. If the ratio of pixels to views is 3 to 1, then the values of two adjacent pixels will reside on an interim basis in each of the shift registers 59 during each of the

25 processing steps.

In a similar manner, the present embodiment may be used to process data when the number of pixels in each concentric ring is either a fractional or a mixed number multiple of the number of views of projection data. For this purpose

30 alternate sets of locator and weighting data may be stored in lookup table 42 and repective views could be processed with the corresponding data. For example, if an addition view VI.5, V2.5, V3.5 etc. were located between each of the views shown in Fig. 6, the locator and weighting data for the

35 interger views (VI, V2, etc) would be different from the locator and weighting data for each of the intermediate views (VI.5, V2.5, etc.). The integer views would be processed with one set of locator and weighting data and then the intermediate views would be processed with the other. Using this approach and the variable delay afforded by shift registers 59, various pixel to view ratios may be accomodated. Further, given the interim nature of the polar cooridnate image formed and the flexibility of the scan conversion process from polar to orthogonal coordinates, it would be possible to vary the number of pixels per concentric ring and the scan conversion to accomodate CAT scan apparatuses producing different numbers of projection views. With respect to the generation of locator and weighting data by the lookup table 42 of Fig. 3, it was mentioned that a memory 45 might only contain data concerning the change in these functions between sequentially backprojected polar coordinate pixels. As explained in reference to Fig. 6, the locator and weighting data is used in accordance with the sequence of pixels being backprojected by the processors. It is clear from Fig. 6 that the sequence of pixels backprojected is a sequence of substantially adjacent pixels. This means that the locator and weighting data does not change substantially between sequentially backprojected pixels, which readily lends itself to the use of a table of difference data simply representing the changes in the locator and weighting data. CONCLUSION

The present invention allows for the advantageous processing of CAT scan data. The polar coordinate image arrangement enables simpler and more reliable backprojection of the scan data. The arrangement is easily adjustable to accomodate scanners producing different numbers of projection views. Further, it readily lends itself to the filtering of ring artifacts and to the simultaneous backprojecting of a multiplicity of sets of projection data.

Claims

WHAT IS CLAIMED IS:

1. A backprojection apparatus for producing image data for a single image from a plurality of sets of projection data produced from different angular positions around a center of 5 rotation within an imaging plane, comprising: means for backprojecting each set of projection data into pixel values for a polar coordinate image, and for summing the corresponding pixel values backprojected from substantially all of the sets of projection data. 102. The apparatus of claim 1, further comprising means for scan converting the polar coordinate image pixel values into orthogonal image pixel values.

3. The improvement of claim 1, wherein the means for backprojecting and for summing includes a plurality of

15 processor means each adapted to simultaneously backproject a separate set of projection data into polar coordinate pixel values.

4. The apparatus of claim 3, wherein the means for backprojecting and for summing includes addressable memory

20 means for storing corresponding locator and weighting data for each polar image pixel location, and means for coupling identical locator and weighting data addressed from the memory means to each of the plurality of processor means.

5. The apparatus of claim 4, wherein the addressable memory 25 means includes a plurality of sets of corresponding locator and weighting data representing different angular orientations between the polar coordinate image and the sets of projection data.

6. The apparatus of claim 4, wherein the means for

30 backprojecting and for summing includes second addressable memory means for storing polar image pixel values; and further wherein each processor means includes third addressable memory means for storing at least one set of projection data, means for addressing the third memory means

35 with the locator data from the first said memory means, and multiplier means for producing the product of projection data from the third memory means and corresponding weighting data from the first said memory means.

7. The apparatus of claim 6, wherein each processor means further includes adding means for summing the products from the multiplier means which correspond to the same polar coordinate pixel.

8. The apparatus of claim 6, wherein the means for backprojecting and for summing further includes adding means for summing the products from the multiplier means with any corresponding pixel values stored in the second memory means.

9. The apparatus of claim 7, wherein the adding means of each processor means includes an input means for receiving pixel values and an output means for coupling addition results, and further wherein the plurality of processor means are coupled in series to provide the addition results from each adding means to the input means of the adding means for the next serially coupled processor means.

10. The apparatus of claim 9, wherein the output means of each adding means includes delay means for storing addition results for a predetermined number of pixels prior to coupling them to the input means of the adding means for the next serially coupled processor means.

11. The apparatus of claim 9, wherein the second memory means includes an input coupled to receive the addition results of the last serially coupled processor means, and an output coupled to the input means of the adding means for the first serially coupled processor means.

12. The apparatus of claim 6, wherein the means for backprojecting includes address generator means for coordinately addressing the first said and second memory means in accordance with polar image pixel locations.

13. The apparatus of claim 12, wherein the address generator means generates addresses in a predetermined sequence, and further wherein the first said memory means contains difference data representing the change in corresponding locator and weighting data between sequentially addressed polar image pixel locations. 14. The apparatus of claim 6, wherein each processor means includes intermediate storage means for storing selected products from the multiplier means.

15. The apparatus of claim 6, wherein the third memory means 5 of each processor means is sufficient to store a plurality of sets of projection data.

16. The apparatus of claim 1, further comprising means for filtering ring artifacts from the summed polar image pixel values.

10 17. The apparatus of claim 1, wherein the projection data consists of a number of sets of data and further wherein the polar image is selected to have a multiplicity of concentric rings each having a number of pixels which is chosen to be an integer, fractional or mixed number multiple of the number of

15 sets of projection data.

18. A method for backprojecting image data for a single image from a plurality of sets of projection data produced from different angular positions around a center of rotation within an imaging plane, comprising the steps of:

20 backprojecting each set of projection data into pixel values for a polar coordinate image; and summing the corresponding pixel values backprojected from substantially all of the sets of projection data,

19. The method of claim 18, further comprising the step of 25 scan converting the polar coordinate image pixel values into orthogonal image pixel values.

20. The method of claim 18, wherein the step of scan converting includes interpolating additional polar coordinate pixel values from the backpro ected polar coordinate pixel

30 values.

21. The method of claim 20, wherein the step of backprojecting includes simultaneously backprojecting a plurality of sets of projection data into pixel values for the same polar coordinate image.

35 22. The method of claim 21, wherein the step of backprojecting includes storing at least one set of corresponding locator and weighting data for the polar coordinate image and using the same locator and weighting data for the simultaneous conversion of the plurality of sets of projection data.

23. The apparatus of claim 18, wherein the projection data consists of a number of sets of data and further wherein the polar image is selected to have a multiplicity of concentric rings each having a number of pixels which is chosen to be an integer, fractional or mixed number multiple of the number of sets of projection data.