DE19952965C2 - Magnetic resonance imaging method with reduced reconstruction error - Google Patents

Abstract

Magnetic resonance imaging method, in which at least one image from an examination object, which is located in a largely homogeneous magnetic field, is obtained by applying a magnetic field gradient G¶m¶, m = 1 of predetermined amplitude and orientation, which serves as a frequency coding gradient, that a high-frequency excitation pulse is sent, which ends at the time t¶m¶, m = 1, that the signal caused by the high-frequency excitation pulse is received at least for a predetermined time T, that this signal is sampled with a scanning bandwidth DELTAf, n> 1 signal values being registered per excitation , the first of which is recorded at a predetermined waiting time Ð at the earliest at the time t¶m¶ +, that this process is repeated for a predetermined number M - 1 magnetic field gradients G¶m¶, m = 2, ..., M that further for at least one of the M processes - for example for the m'th - the first signal value is recorded at the time t¶m¶ '+ Ð that the ma ximal signal bandwidth DELTAf¶s¶ of the examination object is set under all magnetic field gradients G¶m¶, m = 1, ..., M by means of the magnetic field gradients G¶m¶, m = 1, ..., M so that ELDELTAf¶ s¶ <1 applies, and that the scanning bandwidth is selected according to DELTAf> = DELTAf¶s¶, so that the reconstruction error is reduced due to missing contributions of unmeasured signal values in the temporal range of the high-frequency excitation pulses and the waiting time Ð following each high-frequency excitation pulse.

Description

The invention relates to a magnetic resonance imaging method according to the preamble of Claim 1. The method relates to imaging using magnetic Spin resonance in general, however, is primarily intended for use in the field of nuclear magnetic resonance (NMR).

State of the art

In a magnetic resonance imaging method, a time-constant, homogeneous basic magnetic field B ₀ in a predetermined direction - for example along the z coordinate - is generated in a volume to be examined, which contains particles with their own angular momentum (spin), and which generates part of the spins in this Direction. At least some of the spins are excited to resonate by suitable high-frequency pulses. These spins then emit a highly frequented signal, which is preferably received in quadrature, amplified, digitized and processed to give a visual representation of the spin distribution in the volume under investigation. In order to achieve a spatial assignment of the induction signal received from the volume, the basic field B ₀ magnetic field gradients (short gradients) G = ∇B _{z are} superimposed. The signal contribution dS received from a volume element d ³ x is then through after demodulation

given, where ρ _{S represents} the spin density, γ the gyromagnetic ratio, t the time and x the position vector. The function κ is a contrast function and generally depends on various parameters, in particular the relaxation times and the chemical shift. Furthermore, κ is determined by the coil profile and the electronic gain factor. With the magnetic field gradients and acquisition times used for imaging, κ can often be regarded as constant over time, so that κρ _S can be combined to form signal density ρ. The signal received from the entire volume V after excitation is then through

given. Inscribed

the so-called spatial frequency trajectory. The space conjugated to the local space becomes local frequency space (or sometimes called k-space).

Nuclear magnetic resonance imaging is mainly used in the medical field. There Shortening the recording time plays a special role. On the one hand, through a increased recording rate motion-dependent image artifacts reduced, on the other hand, dy Namely processes can be observed, which can provide physiological information, for example nen. There are a large number of suggestions for measurement methods for rapid imaging. She was reading sen with regard to the spatial frequency trajectory used, the type of signal used and the number of high frequency excitations required. The increase in In most processes, the uptake rate is achieved by the fact that after an appeal Induction signal generated by using suitable magnetic field gradient pulses or High frequency pulses are dephased and rephased several times. However, this creates problems and Disadvantages in terms of image quality. Rapidly oscillating magnetic field gradients require a lot powerful and costly gradient systems and cause difficulties due to the eddy currents generated on the measurement object. These lead to geometrical aberrations, Image artifacts, signal loss and are the cause of nerve irritation, making security limit this strategy. With the echo formation by radio frequency pulses, pulse amplitude calibrations are to be carried out, and here too a maximum effect limiting the rate of energy absorption. With this type of rephasing you can additionally no continuous time series are recorded, since the magnetization after the Da The opportunity to relax must be given. With all procedures based on multiple dephasing and rephasing of the induction signal results in a loading limitation of the spatial resolution if the self-diffusion or the relaxation to a considerable extent Signal decay over the period of data acquisition leads. Microscopic and macroscopic Magnetic field inhomogeneities are often the cause of a severely impaired image quality. Hy Bridge pulse sequences alleviate these disadvantages, but make a correction to the inevitably Amplitude and phase modulation occurring in spatial frequency space is necessary. Because of the above Most of the proposed measurement methods have only very limited difficulties found in clinical routine. Spin echo imaging applies because of its high image quality still standard and remains the basis of medical diagnosis.

The disadvantages of the methods mentioned are avoided if the free induction signal (FID) is recorded instead of one or more echoes. In the case of recording the free induction signal, the spatial frequency space trajectory is complete for a single excitation

given, where G was assumed to be constant. Depending on the type of excitation pulse, the signal value corresponding to the volume integral of the signal density is k = 0

either within the period of the suggestion, at the end or afterwards. In the latter case, the excitation pulse is called prefocusing. The time zero must always be selected accordingly. In order to be able to reconstruct an image of the measurement object, a series of M different gradient orientations have to be run through, so that the spatial frequency space trajectory of the entire measurement as

can be written. The signal recording extends over a predetermined time interval, the duration T of which depends on the desired spatial resolution. The time zero associated with the m-th excitation is designated with t _m . With a short block pulse, you can use the end of time here. If we consider only a single excitation in the following, we set t _m = 0. The amplitude of the gradients is preferably the same for all orientations. Hence G _f = | G _m | for m = 1,. . . , M, where G _{f is} called the frequency gradient gradient. The signal bandwidth Δf _{S is} determined by the amplitude of the gradients. If we think in the case of three-dimensional acquisition, the measurement object is enclosed in a sphere at the origin with the smallest possible radius R, the signal bandwidth is always less than or equal to γG _f R / π. We define the signal bandwidth as this maximum value, so

In the following, we use the terms signal bandwidth, effective bandwidth and useful bandwidth as synonyms. In the case of the two-dimensional acquisition approximately in the xy plane, the extent of the measurement object along the z direction is irrelevant. The sphere can therefore be replaced by a cylinder with the same radius oriented along the z direction. As is known, a discrete temporal sampling with a step size δt = 1 / Δf _S is sufficient for the reconstruction of such band-restricted objects, with quadrature reception being assumed. For the sampling rate (sampling bandwidth) Δf set on the spectrometer, Δf = νΔf _S , where ν with ν ≧ 1 defines the degree of oversampling.

In a method which is based on the registration of the free induction signal, the problem of missing data points now arises in the vicinity of k = | k | = γG _f t = 0, because immediately after the excitation pulse, signal reception is impossible for a certain time interval, the so-called receiver dead time. In the following, we understand the receiver dead time or waiting time to be the time interval τ at which, at time τ, calculated from the end of the previous high-frequency excitation pulse, a signal value can be recorded which is so far free from interference that it can be used for the reconstruction. One will preferably choose the shortest such time interval under the given experimental conditions. The same value for τ will preferably also be used for all suggestions. Otherwise, the waiting time τ means the minimum of these times. When we speak in the following of measured signal values, we are always referring to the signal values in the narrower sense, which in principle can also be used for reconstruction and not those which have to be rejected because of a disturbance. According to this definition, the first measured signal value is always at time τ (or afterwards), even if signal values are recorded in the interval 0 <t <τ, which are not used for the reconstruction. Due to the finite receiver dead time, the data points in the vicinity of k = 0, which are regarded as extremely important, cannot be measured. It is expected that this will lead to significant reconstruction errors.

The idea of using the free induction signal for image acquisition has been missed picked up on.

[1, 2] specifies a method with three-dimensional, radial acquisition technology. With a basic field strength of B ₀ = 93.8 mT, 900 projections were recorded in a total measuring time of 12 minutes and a matrix with a resolution of 33 × 33 × 33 pixels was reconstructed from them. So it is not a quick process. Above all, it is not disclosed how the above-mentioned problem of missing signal values in the vicinity of k = 0 is solved. In this regard, no technical teaching can be derived from the publications [1, 2].

[3, 4] specifies a further method which is intended to allow a single layer to be imaged in a similar manner. The gradient orientation is not varied spatially, but circularly. The first digitization point is recorded 8 µs after the end of the excitation pulse. According to the definition made here, τ = 8 µs. This time interval corresponds to the reciprocal of the specified useful bandwidth of Δf _S = 125 kHz. The sampling rate Δf is 1 MHz. The reasoning given in [3] regarding the influence of the data point at k = 0 on the reconstruction result is neither correct in content nor is the numerical value given for the weight of the signal value at k = 0 applicable. This will be clarified in the course of the description of the present invention. While the problem of the missing data points in the vicinity of k = 0 is not seriously discussed in [3] nor is it presented in a convincing way to what extent the indicated procedure could lead to an artifact-free reconstruction, [4] a method to determine the missing measuring points in the vicinity of k = 0. This method evaluates pixels that are in the noise. In addition, the phase of the signal at t = 0 must be known. Missing measuring points can possibly be estimated with the specified algorithm. How well this succeeds experimentally remains open here, since the algorithm is only demonstrated using synthetic, noise-free data. The specified accuracy of 10 ^-6 therefore only reflects the numerical uncertainty of the implementation of the algorithm on an electronic computer system and does not allow any conclusion to be drawn about the experimental applicability. Another method is proposed in [5], which goes back to [7]. With this method, several parameters have to be professionally optimized for each image data set and additional measurements (test projections) are necessary, a procedure that opposes the routine use of the measurement method. It is striking that authors of the same working group continually present different approximation methods without the experimental error for the determination of missing signal values and the resulting reconstruction error being disclosed for one of these correction methods. This gives the impression that the problem of the missing signal values in the vicinity of k = 0 could not be solved in a satisfactory manner. Furthermore, the potential of a method based on the registration of the free induction signal is not recognized. The method specified in [3, 4, 5, 6] appears only suitable for a few special applications in the manner shown. In the measuring method described, a layer-selective recording is achieved in that the magnetization outside the measuring layer is destroyed by saturation. However, the saturated volume is generally much larger than the volume of the measuring layer, so that there is soon an unwanted signal contribution by the relaxation, which leads to drastic image artifacts. The measurement must therefore be carried out extremely quickly. With the specified 32 projections, however, even when synthesizing the conjugate complex data via the known signal relationship S ( k ) = S (- k ), only a 20 × 20 image matrix can be correctly obtained. This resolution is far from sufficient for clinical applications.

Another method, which is based on the registration of the free induction signal, is that specified in US patent application [8]. Here those around k = 0 immeasurable signal values by separate measurements varying the gradient amplitude certainly. Additional measurements are therefore necessary.

None of the above-mentioned methods based on the reception of the free induction signal den, so puts a satisfactory solution to the problem of missing data points in the vicinity of k = 0 and the resulting reconstruction error. The These methods are therefore not used in practice, even though they are extremely possess desirable properties. Rather, experts believe that the missing signal values in the vicinity of k = 0, which are classified as extremely important can practically not be approached with sufficient accuracy to always be pictures satisfactory quality.

Object of the invention

It is the object of the invention to find a satisfactory solution to the problem of feh are signal values in the range of the excitation pulse and the receiver dead time and from resulting reconstruction error. In this way, an extremely fast Measurement methods for three-dimensional or two-dimensional imaging of an object provides that eliminates the disadvantages of the known measuring methods mentioned. This task is indicated by a magnetic resonance imaging method with the in claim 1 resolved characteristics. Individual advantageous embodiments of the invention are the subject of subclaims. The essential properties of the invention can be summarized as follows sum up.

• A) The acquisition speed is comparable to that of echoplanar imaging.
• B) The signal-to-noise ratio per unit of time is comparable to that of the FLASH pulse sequence.
• C) The image quality is comparable to that of conventional spin echo imaging.
• D) The influence of signal loss due to phase dispersion is extremely small.
• E) The influence of signal loss due to transverse relaxation is extremely small.

An invaluable advantage of the method is that there are no special requirements the performance of the gradient system. So in principle it can be on everyone common tomographs are used.  

Description of the invention

The entire object under investigation is stimulated by regularly recurring, broadband high-frequency pulses. For example, block pulses of short pulse duration (e.g. 2 µs) can be used. The induction signal caused by the high-frequency excitation pulses is received immediately after the end of the receiver dead time (waiting time) τ and digitized with a predetermined scanning bandwidth Δf over a predetermined acquisition time T. Because of the finite settling time of the analog-digital converter, it can be advantageous to let it run without interruption for the duration of the entire experiment and to only switch off the reception during high-frequency excitations. In principle, sending and receiving can also be handled via two different high-frequency channels. A magnetic field gradient of preferably constant amplitude G _{f is} constantly switched on for spatial coding. It does not have to be switched off during the excitation phase because the high-frequency pulses ensure sufficient broadband excitation. The speed of the method is based on the fact that the magnetic field gradients never have to be switched off or reversed and that successive gradient orientations differ only by a small increment δ G. After each data acquisition, there is therefore only a very small dead time, which is due to the fact that a new gradient orientation must be set before the next excitation. As soon as this is reached, the next high-frequency pulse is sent immediately and the next data acquisition is carried out. The process of excitation, the subsequent signal reception and the creation of a new gradient orientation is repeated with a predetermined repetition time T _R until a predetermined number of M gradient orientations has been completed. In the two-dimensional case, for example, a gradient trajectory can be used

at. In the three-dimensional case one can use s _m = (2m - M - 1) / M

use. The latter trajectory was related to the three-dimensional high frequency excitation proposed [9]. It leads to a largely isotropic distribution of measurement score per unit solid angle, and it can be run through very quickly.

Using a realistic numerical example, it should be shown that the dead times of the pulse sequence are actually very short: With an image area of 256 mm, a data matrix of N × N or N × N × N points (N = 256), a scanning bandwidth of Δf = 125 kHz and a gradient switching time of 40 mT / m per millisecond results, for example, for the frequency coding gradient G _f ≈ 11.5 mT / m, for the relative gradient change ΔG / G _f = 2 / N ≈ 0.008 and thus a switching time of around 2 µs. This small dead time can now also be made to disappear, namely by the fact that the magnetic field gradients are not kept constant for the duration of an acquisition period, but by continuously changing them so that at the end of a data acquisition the next orientation is already achieved . This embodiment of the invention results for the example mentioned

as a gradient change per time. This is around four orders of magnitude below the switch times that are necessary in echoplanar imaging. It can be seen from this that the Eddy currents and the gradient switching noises of the pulse sequence according to the invention ver can be neglected.

It will now be explained how to solve the problem regarding the missing signal values in the vicinity of k = 0. To do this, we will examine the properties of the reconstruction specification in detail below. The relationship between the signal S and the signal density ρ, which is proportional to the transverse magnetization m ₊ , is through in the two-dimensional case

and in the three-dimensional case

given.

For the two-dimensional case we consider the reconstruction of a circular disk with radius R and signal density one at the origin. The signal calculates itself

where J ₀ and J _{1 represent} Bessel functions, which by

are defined. The reverse is

For the three-dimensional case we consider the reconstruction of a sphere with radius R and signal density one at the origin. The signal for this is

with the reversal

For r = 0 one has to add a factor e ^{- α z} with α <0 in the integrand to force the convergence.

As is known, a discrete scan with a step size is sufficient for the reconstruction of such spatially restricted objects

where ν defines the degree of oversampling. Usually the data acquisition is interrupted after N / 2 points, so that a maximum of up to a resolution of

can be reconstructed. For the win kelkrement δϕ or the number of projections M results in δϕ = 2π / M = 2 / N.

The integrals can be calculated, for example, by rear projection. This is done in the two-dimensional case

executed, where S (-k, ϕ + π) = S (k, ϕ) is used. The integral over k is therefore called the FOURIER integral

interpreted with respect to the variable t = xcosϕ + ysinϕ. It should be noted that the variable t does not have the meaning of time here. In fact, as already mentioned, the signal pickup will take some time

canceled so that one is more precise

must write, whereby

a filter with the impulse response

is. Since H (k) is restricted to [-K, + K], a FOURIER decomposition is according to

possible. With the help of

for H (k) this results in the series expansion

The situation in the three-dimensional case is completely analog. Here one obtains the equation by means of S (-k, ϕ + π, π - θ) = S (k, ϕ, θ)

The filter

has the impulse response

from which one by means of

to be led.

If we suppress the angular dependence of Λ and S for brevity, the following results regardless of the dimension:

 however, as a projection of ρ, like ρ, is limited to the interval [-π / δk, + π / δk], so that the sum actually breaks off from a certain index N '≦ N / 2 and the convolution h.

in other words

This sum is known to be the expression

equivalent, where F _N denotes the discrete FOURIER transformation with N points. The fact that the FOURIER development for the filter function stops at a certain index has different consequences in the two-dimensional and in the three-dimensional case. This is related to the fact that the convergence of the series in the two-dimensional case is not possible to differentiate the filter function H (k) ~ | k | is slower at k = 0. Indeed it is

so that the ratio of the weight at point k = 0 to the nominal weight at k = δk goes towards 1 / π ² ≈ 0.1013. In the two-dimensional case, this results in noticeable, low-frequency deviations, including the shift in the zero line. In the three-dimensional case, on the other hand, the series converges quickly to the filter function H (k) ~ k ² , which runs smoothly at k = 0, so that such an effect cannot be observed here.

In order to test the reconstruction, the integrals 15 and 17 are evaluated numerically in the following, namely by discretization dz = dkR = π / ν analogous to the experimental procedure. The number of digitization points is N / 2 = ν. 512. The result is shown in FIG. 1. The deviation δ from the target function in the range r / R = 0.25-0.75 is calculated and averaged at 100 equidistant points. The result is summarized in the following table.

As you can see, in the three-dimensional case the target function is achieved within the tolerance limit. The standard deviation only mirrors the oscillations in the spatial domain like that which result from the clipping of the signal from a certain index. With N / 2 = ν. 16384 digitization points, the deviations drop to (0.1 ± 2.0). 10 ^-6 . In the two-dimensional case, on the other hand, there is a significant discrepancy, which in terms of amount

can be estimated. With increasing oversampling ν this quickly goes to zero. With a fourfold oversampling, the reconstruction error already drops below the percent mark and is therefore practically in the area of noise. The general conclusion is as follows:
In the three-dimensional case, the signal value at k = 0 is not included in the reconstruction, and there is no reconstruction error. In the two-dimensional case, a reconstruction error arises even at a normal sampling rate, which is in a leading order for an image area 2R

is. It can be made arbitrarily small by suitably high selection of the oversampling ν.  

It is now essential to relate the oversampling ν to the receiver dead time τ. We define the maximum oversampling ν _Max

This is the highest oversampling value ν at which the signal value

can still be measured at a signal bandwidth Δf _S predetermined by the frequency coding gradient G _f and a predetermined receiver dead time τ. From an experimental point of view, ν can never exceed ν _Max in the above calculations, although the induction signal can in principle be sampled in the time range t <τ with a sampling rate Δf »1 / τ. We give an example. With a signal bandwidth of Δf _S = 125 kHz and a dead time of τ = 2 µs, the maximum oversampling is ν _Max = 4. The sampling rate Δf set on the spectrometer may well be 2 MHz, ie clearly above ν _Max Δf _S = 500 kHz . A high oversampling in the time range t <τ will generally even be indicated in order to reduce the distortion of the signal by the low-pass filter. It also considerably facilitates the extrapolation of missing signal values mentioned below. As is known, the distortion of the signal by the low-pass filter can also be reduced in that a time interval of a suitable size is inserted between the switching on of the reception and the registration of the first digitization point, so that the signal values are sampled in the vicinity of the zero crossings of the transient function.

In order to further clarify the meaning of the present invention, we want to correct the misleading reasoning given in [3] regarding the weight of the signal value S (0). It is stated there that the unmeasurable signal value at k = 0 is necessary for the reconstruction. This is justified with a geometric argument. The authors of [3] are of the opinion that each signal value must be weighted in the spatial frequency space with the area element surrounding it. In the two-dimensional acquisition, the weights would result from this with a step width δk

the weights for the three-dimensional acquisition

As is clear from the above explanations, this is incorrect, because the ratio of the weights between the first signal value (i = 0) and the second signal value (i = 1) is not 1/8 in the case of the two-dimensional acquisition, but approaches with increasing oversampling 1 / π ² on. It is also not the case that the deviations, as in the one-dimensional case, can only be explained by a shift in the zero line. The other signal values in the vicinity of k = 0 are also given a weight which is albeit much weaker, so that low-frequency deviations of higher order result. This is clearly evident from FIG. 1 and depends on the finite number of FOURIER coefficients for the filter function H (k) ~ | k | together. The fact that the reasoning expressed in [3] is incorrect is completely evident when one considers the three-dimensional case: Here the signal value at k = 0 is actually not included with any finite weight, but with w _3D (0) = 0. At In all considerations in [3, 4, 5, 6, 7] there is no decisive knowledge about the magnitude of the influence of the unmeasurable signal value at k = 0 on the reconstruction result. However, this knowledge only results in the technical teaching formulated in the present invention. In order to shed further light on this point, we consider measures to suppress the reconstruction error below.

• 1. (α) As already mentioned, the simplest measure to reduce the reconstruction error is to choose the product between the receiver dead time and the signal bandwidth τΔf _S = 1 / ν _Max as small as possible. With the sampling rates of 50-100 kHz common in the clinical field and receiver dead times of about 2 µs in the prior art, this is readily possible. With ν _Max = 4, a ratio of the signal to the noise (SNR, signal-to-noise ratio) of more than 200 would be necessary in order to notice the reconstruction error. In this case, no further correction needs to be carried out at all.
• 2. (β) In the lowest order, the reconstruction error in the two-dimensional case consists in a shift of the zero line by
  In order to get an idea of the influence of the contribution of the signal value at k = 0, one can carry out this correction, but instead of the unknown signal value S (0) the first measured point
  is used. In the example of the circular signal density distribution, the deviation from the target function δ _{2D is} reduced to the values listed in the following table under δ ' _2D .
  The improvement achieved is noteworthy. Even with this rough estimate, the reconstruction error is below the alcohol limit in all cases. However, the higher order deviations are not corrected.
• 3. (γ) A further measure to suppress the reconstruction error is the extrapolation of missing measurement data. The method of linear prediction [10], for example, is suitable for this purpose, in which coefficients c _j (j = 1,..., J) are determined such that the deviations δ _l in
  get as small as possible. Missing data points are then estimated using these coefficients. For the application of this method, it is extremely helpful to record the signal significantly oversampled in the time range t <τ. In order to be able to assess the quality of the extrapolation, we compare the extrapolated signal values s _m (m = 1,..., M) at the point k = 0 of M = 1024 projections, which were recorded in three-dimensional acquisition technology, with the true one Value s _{0 of} the signal at the point k = 0. The other parameters are Δf _S ≈ 100 kHz, Δf = 2 MHz, τ = 4 µs. The true value for S (0) was determined from a further 16 projections with the magnetic field gradient switched off. In this case, the signal varies only slightly over time. As can be seen in FIG. 3, there is the signal contribution of the test object superimposed by a solid-state signal from the coil. S (0) can be determined precisely by extrapolation. The fluctuation range for the signal amplitude of S (0) is around 0.7% in the present case. The end of the 2 µs long block pulse is selected as the time zero. The determined values s _m / s ₀ are shown in FIG. 4. The mean
  is summarized in the following table for different values of L and J.
  The fluctuation around the true value s ₀ is consistently around 3%. If only the first L = 64 digitization points are received, the best result is achieved since the noise component is then low. As the number of digitization points taken into account increases, the estimate for S (0) drops somewhat below s ₀ , since the solid-state signal from the coil is then received with too little weight. No clear trend can be seen for the number of coefficients J used. A medium number seems appropriate. The reconstruction essentially only includes the mean of the extrapolated values for S (0). With a signal bandwidth of around 100 kHz, a receiver dead time of 4 µs and a sampling rate of 2 MHz, the error of the extrapolation can therefore be estimated experimentally with typically one percent. The reconstruction error decreases by two orders of magnitude by using the linear prediction method under these conditions and is therefore well below the alcohol limit. It has been shown experimentally that artifact-free images can be reconstructed with the method of linear prediction if τΔf _S <1.

Any extrapolation method can also be used iteratively. One first determines the fairly reliable mean for S (0) from some or all of the projections and, in a second step, determines (oversampled) measured values in the range 0 <t <τ for each projection using a suitable method. Alternatively, as already mentioned, S (0) can also be obtained by direct measurement with the magnetic field gradients switched off. There is only an insignificant increase in the measurement time by around one millisecond. It should be mentioned that the approximation of oversampled signal values in the range 0 <t <τ in the case of Δf <Δf _{S is} no problem experimentally, since these signal values can be approximated even more precisely than S (0) itself. In practice it is recommended to choose τΔf _S = 1 / ν _Max as small as possible, e.g. τΔf _S = 0.8, τΔf _S = 0.5, τΔf _S = 0.25, τΔf _S = 0.125 or τΔf _S = 0.05 and additionally carry out a (rough) extrapolation. This can also be done in real time.

The discussion of the above correction methods does not aim to highlight the quality of a special algorithm. On the contrary, it is intended to show that the quality of the correction method is virtually irrelevant when choosing a suitably high oversampling ν _Max . This makes the practical applicability of the process independent of the properties of special approximation or extrapolation processes. This makes the process very robust. The object of the invention is thus achieved and the disadvantages of the methods described in [3, 4, 5, 6, 7] are eliminated. We summarize the following technical teaching:
The omission of the signal value at k = 0 leads to a reconstruction error in the two-dimensional case, which can be brought completely below the noise level by a sufficiently high oversampling ν _Max and possibly also by a (rough) extrapolation or approximation. In the three-dimensional case, the signal value at k = 0 makes no contribution at all, so that there is no reconstruction error.

This eliminates a long-held prejudice that has prevented an advantageous one seriously consider this measurement method. We now turn to special Properties and refinements of the invention.

1. Measuring time

With the method there are practically no dead times due to gradient switching processes. It is therefore very quick. Eddy currents and gradient switching noises are negligible. The measuring time is calculated as follows. With an image matrix of N ⁿ (n = 2, 3) points, M ≈ πN ^n-1 projections must be recorded. The repetition time at a sampling rate of Δf, neglecting the high-frequency pulse duration T _R = (N / 2) / Δf, so that the total measuring time by

given is. At N = 128 and Δf = 125 kHz, this gives T _2D ≈ 206 ms and T _3D ≈ 26 s. In the two-dimensional acquisition with N = 64 and Δf = 500 kHz, the total measurement time T _2D ≈ 13 ms can be specified as the limit of the achievable time resolution. In principle, this could be halved again by using the signal relationship S ( k ) = S (- k ). However, the achievable signal-to-noise ratio (SNR) will rarely make such a measure seem reasonable. Such an exceptional case may exist if the signal-to-noise ratio can be increased significantly, for example by saturating the electron resonance.

2. Signal behavior and contrast

With an excitation angle α, a repetition time T _R , a longitudinal relaxation time T ₁ and a thermodynamic equilibrium magnetization m _∞ , after a short transient phase, an equilibrium state is reached in which the amplitude of the transverse magnetization component m ₊

given is. It is assumed that there is no echo formation due to the preferably low excitation angle and the varying magnetic field gradients. At higher excitation angles, echoes can be suppressed in a known manner by stochastic variation of the phase of the excitation pulses. The contrast is determined by the spin density and the longitudinal relaxation time. By varying the deflection angle, a T ₁ contrast of a freely selectable form can be brought about. The signal amplitude is determined by the choice of the ERNST angle

maximized. In the case of negligible transverse relaxation, the signal-to-noise ratio per unit of time is smaller by a factor of 1 / √2 compared to the field echo pulse sequence; with an echo time T _E ≈ T * | 2/2, the signal-to-noise ratios per unit of time are approximately the same.

3. Contrast preparation

The contrast of the images can be influenced in a known manner via a gradient and / or high-frequency pulse sequence which precedes the measurement or interrupts it at selected points. Among other things, this can be based on

• a) diffusion (D),
• b) the speed (ν),
• c) the longitudinal relaxation time (T ₁ ),
• d) the transverse relaxation time (T ₂ ),
• e) the effective transverse relaxation time (T * | 2),
• f) chemically selective excitation (CHESS),
• g) streak or grid excitation (tagging),
• h) the magnetization marker (bolus tagging),
• i) magnetization transfer,
• j) adiabatic inversion (adiabatic passage).

Using the contrast preparations belonging to the prior art, further physical or physiological parameters such as the temperature (via T ₁ or D) or the perfusion (for example via T ₁ or T * | 2) can be determined. A new data set can be calculated from a series of images with varying contrast preparations. Known examples are parameter maps of the relaxation times, the diffusion constant or the speed. Subtraction images can be calculated to suppress an unwanted signal component.

4. Image properties

The amplitude distribution caused by the excitation corresponds to that which is present in the field echo pulse sequence. However, the imaging properties are essentially the same as those of a spin echo pulse sequence when the echo time T _E disappears. This can be seen from the fact that a pseudo-echo can be composed of two induction signals with oppositely polarized magnetic field gradients. Differences in the spin echo pulse sequence concern the influence of relaxation, phase dispersion and chemical shift. Of particular note is the favorable behavior towards magnetic field jumps at interfaces.

5. Time-resolved imaging

The measuring method can be used in constant repetition, since the Magne tization is in a state of equilibrium. It is therefore suitable for applications in real-time imaging, interactive imaging and observation dy naming processes.

• a) Stroboscopy: By suitable segmentation of the gradient trajectory and by synchronization with an external signal, a stroboscopic recording of recurring processes can be obtained with an extremely high temporal resolution. The highest temporal resolution corresponding to the repetition time T _R is obtained, for example, if a certain magnetic field gradient is kept constant for the duration of an entire cycle and the next magnetic field gradient is set shortly before the following cycle. Alternatively, different projections can be run through per cycle, which are then supplemented in the course of subsequent cycles.
• b) Fluoroscopy: If the same gradient trajectory with M high-frequency excitations (projections) is repeated in a repetition time T _R , an image data set from the previous M induction signals can in principle be patterned after each high-frequency excitation
  be calculated. If a sufficiently powerful reconstruction unit is available, this can be done while the measurement is running. If low-resolution intermediate images are to be reconstructed, it is advisable to advance in larger increments in such a way that all frequency data are only acquired after several cycles. For example, with M = 256, the projection partial sequences (1, 4, 7,..., 256) (2, 5, 8,..., 254) (3, 6, 9,..., 255) Reconstruct three subsampled or reduced-resolution images. This has the advantage that a decision must be made only after the experiment as to whether a high temporal resolution with low spatial resolution or vice versa is desired. This procedure is also advantageous in the case of rapid signal changes since it reduces image artifacts. It also suppresses echoes.

6. Solid-state imaging

The line broadening δf _{T * | 2} due to the transverse relaxation, characterized by a time constant T * | 2, depends on the dimension n (n = 1, 2, 3) of the experiment

With a signal bandwidth of 500 kHz and 128 pixels (e.g. δr = 0.5 mm resolution at G _f = 183.5 mT / m) corresponding to a frequency interval of δf ≈ 4 kHz per pixel, the three-dimensional variant of the invention can already amorphous solids with relaxation times of

be sharply reproduced. The imaging of crystalline solids becomes tangible when the receiver dead time τ ≦ 0.5 µs.

7. Imaging with special cores

The method is suitable for imaging with nuclei that deliver a short-lived signal, such as ¹⁷ O and ²³ Na.

8. Imaging with contrast media

The method is particularly suitable for imaging with contrast media. Their effect is based on a higher equilibrium signal due to the shortened T ₁ time. The opposing influence of the accelerated transverse signal decay has a much weaker effect in the present invention, in contrast to measurement methods which are based on the recording of echoes, so that the range of the clear association between signal strength and contrast medium concentration over a larger range of T ₁ values preserved. If the short excitation pulses fail to saturate the magnetization sufficiently, you can insert saturation pulses at regular intervals. Particularly noteworthy applications in this context are the observation of contrast medium flooding in the kidneys and the projective vascular imaging.

9. Microscopy

The achievable spatial resolution in the method according to the invention is approximately twice as high as in the echo method due to the low signal attenuation by diffusion. In the border area of high spatial resolution, the signal-to-noise ratio per unit of time is also more favorable than with echo methods. For this reason, the measuring method according to the invention is well suited for microscopy. The line broadening δf _D due to the diffusion is dependent on the dimension of the experiment

where D is the diffusion constant and T is the acquisition time per induction signal. With a gradient strength of G = 200 mT / m, the line broadening for protons (γ / 2π = 42.577 MHz / T; D = 2.10 ^-9 m ² / s; µ / T = 124 Hz) leads to a resolution limit of approximately δr = 10 µm.

10. Imaging with polarized gases

The diffusion constant of gases is around four orders of magnitude higher than that of liquids. The method according to the invention is therefore extremely suitable for imaging with polarized gases, for example for functional imaging of the lungs. The line broadening δr _D for two typical nuclei used for imaging the lungs is given in the following table, where G = 20 mT / m and D = 2. 10 ^-5 m ² / s was assumed.

11. Angiography

The method according to the invention is insensitive to signal weakening, which is caused by spin motion. This signal loss is caused by a phase dispersion due to vortex formation, turbulence or steep speed gradients and leads to image deletions, which leads to incorrect assessment of vascular ver leads to narrow ties. This is a very serious disadvantage of the known nuclear magnetic resonance Process compared to the X-RAY process, which is therefore still a means the choice is used for unequivocal diagnosis. In the Ver drive occur significantly weaker signal cancellations, so that it is excellent suitable as an angiographic measurement method. These vascular representations can be viewed with the help of Contrast agents or by one of the known magnetization preparation methods be won. In one of these known methods, the longitudinal magnetization tion prepared in such a way that its amplitude is proportional to the speed in a certain direction. This includes, for example, acquisitions preceded by pulse sequences of the type 90 ° | α-G-90 ° | ß with suitable phases α and β and combined. Another known way is to take two pictures of an area to perform, with one of these recordings the magne flowing into the area is inverted beforehand. The appropriate combination then provides an angiogram. When using contrast media for vascular imaging, pictures can be taken after the known methods of digital subtraction angiography (DSA) of the X-ray technique create.

12. Projective imaging

The two-dimensional variant of the method is excellent for obtaining projective Suitable recordings. Projective recordings are advantageous if a high intrinsic contrast, such as in perfusion studies or angiograms with the help of Contrast agents or in processes in which a certain signal component can be preparation is suppressed. It should be remembered that in clinical practice X-ray images still used today at a profit, nothing more than fluoroscopic images,  are projective recordings. Such projection recordings come across the use of field echoes on considerable difficulties, since it is due to Ma magnetic field inhomogeneities comes to signal cancellations via the projection direction. At a method that is based on the registration of the free induction signal is the Si gnal at k = 0 regardless of its frequency separation in phase, so this effect here is not observed. A possible variant is alternating projections perform along different spatial directions.

Description of the figures

14 figures are attached.

• 1. The qualitatively different reconstruction results are illustrated in FIG. 1 in the two-dimensional (2D) and in the three-dimensional (3D) case. This fact is examined in detail in the course of the description of the invention. First, the signal of a signal density distribution was calculated analytically, which for the radius r <R is constantly equal to one and otherwise zero. A signal density distribution p was calculated from this signal using the appropriately discretized reconstruction instructions. N / 2 = ν per induction signal. 512 digitization points with two and sixteen times oversampling ν are used. In the two-dimensional case there is a visible reconstruction error at ν = 2, which has practically disappeared at ν = 16. In the three-dimensional case, the reconstruction is error-free for all values of the oversampling ν. The slight oscillations of the calculated signal densities are due to the finite number of digitization points.
• 2. FIG. 2 shows the signal S, recorded in quadrature, of an examination object, which has a signal bandwidth of Δf _S ≈ 100 kHz. In all experiments shown here, the sampling rate is Δf = 2 MHz. Four acquisitions were averaged for each projection direction. Block pulses with a duration of 2 µs and an excitation angle of approximately 1 ° were used for excitation. The signal reception is free of interference 2 µs after the end of the excitation pulse (at t = 0). However, the first three digitization points must be discarded due to the transient response of the analog-digital converter, so that the effective receiver dead time (waiting time) is τ = 4 µs. Extrapolated signal values are also shown. The true value of the signal s ₀ at t = 0 was determined by a measurement with the magnetic field gradient switched off (see FIG. 3). The standardized time signal S (t) / s _{0 is} plotted.
• 3. FIG. 3 shows the time course of the signal amplitude S of the same examination object when the magnetic field gradient is switched off. The signal contribution of the object under investigation is superimposed by a solid-state signal from the coil (T * | 2 = 297 µs). The time signal is normalized to the extrapolated signal amplitude s ₀ at t = 0, which was determined from 16 such signal curves with a relative error of 0.7%.
• 4. FIG. 4 shows the ratio of 1024 extrapolated signal values s _m for t = 0 to the true signal value s ₀ at t = 0. For this purpose, M = 1024 projections of the above-mentioned examination object were recorded using a three-dimensional acquisition technique. The true value s ₀ is based on measurements with the magnetic field gradients switched off (see FIG. 3). The method of linear prediction using the first L = 64 data points and J = 16 coefficients was used for extrapolation. This method is explained in more detail in the description of the invention. The average ratio s of the extrapolated signal values s _m to s ₀ here is s = 1.002 ± 0.034.
• 5. Fig. 5 shows profiles and images of a sample tube, which were obtained with the two-dimensional variant of the invention. The sample tube has an inner diameter of 10 mm and a wall thickness of 1 mm and contains a substance that has a disintegration time of T * | 2 = 180.0 ± 0.2 µs. In the two-dimensional variant of the invention, this corresponds to a line width of 1.355 kHz or a location blur of 347 μm with a frequency coding gradient of G _f = 91.75 mT / m. We define all line widths as the width of the curve halfway up its maximum (FWHM). Δf _B denotes the frequency width here and below, which corresponds to an image area of 2R = 64 mm. The display of the profiles contains images with 32 × 32 pixels each and a pixel width of 0.5 mm. At the bottom left is a picture that was obtained with a field echo pulse sequence (FE) with an echo time of T _E = 1.1 ms and an excitation angle of α »1 °. On the right there are images that were created with the method according to the invention (FID). The bandwidth Δf _{B is} noted under each image. The integral was used for reconstruction
  discretized directly. M = 512 projections with an angular increment of δϕ = 2π / M are used. The acquisition time per induction signal amounts to T = 1024 µs. At Δf _B = 62.5 kHz, the image is still blurred because the line broadening is 1.4 mm due to the signal decay. The same applies to the recording at Δf _B = 125 kHz, at which the location blur is still 0.7 mm above the pixel width. At Δf _B = 250 kHz the line broadening drops to 0.35 mm and a sharp image is obtained. This can be seen more clearly from the profiles. At the highest band width, the edge of the tube is shown without grinding. The image amplitude does not immediately disappear on the edge of the tube. The reason for this is a solid-state signal from the plastic wall of the sample tube. Its decay constant is still below that of the sample solution, so that the image of the tube wall at Δf _B = 250 kHz is still not clear. If physiological saline solution is used as the sample solution, this effect becomes more apparent because the two signal components differ more in their decay time (see FIG. 7).
• 6. FIG. 6 shows a profile of the above-mentioned sample in two different scalings at Δf _B = 250 kHz. During the reconstruction of the profile shown, the acquisition time T per induction signal was limited to 370 µs in order to achieve the optimal signal-to-noise ratio. With this choice of T, the frequency resolution corresponds exactly to the line broadening due to the signal decay. In the case of negative coordinate values, weak solid-state contributions from the coil can still be seen at the level of the noise in the vicinity of the examination object. The structures just barely recognizable at the edge of the area shown can be traced back to the finite number of projections.
• 7. With the two-dimensional variant of the invention, FIG. 7 shows profiles and images of a sample tube with the dimensions already mentioned above. The tube contains physiological saline (NaCl 0.9%). If the signal bandwidth is low, the solid-state signal of the tube wall provides hardly any picture contribution. As the signal bandwidth increases, its weight increases, as can be seen from the excessive amplitude in the area of the tube wall. At Δf _B = 333.3 kHz the representation of the tube wall is still not clear, so that one has to conclude that the decay time of the solid state signal from the tube wall is below T * | 2 ≈ 100 µs. To the right of the profiles is schematically indicated how the picture contributions of tube wall and sample solution overlap. Below the presentation of the profiles is a series of pictures of the examination object. The corresponding bandwidth Δf _B is given under each picture. A 32 × 32 matrix with a pixel width of 0.5 mm is shown again. 512 projections were used.
• 8. FIG. 8 shows profiles of the above-mentioned sample tube with saline for Δf _B = 62.5 kHz and an acquisition time of T = 2048 μs per induction signal over a larger area. The solid curves show the reconstruction result when using an exponential filter e ^{-t / τ _F} for the time signal. The filter constant τ _F is chosen so that the one-dimensional line broadening is precisely the frequency width of a pixel
  corresponds to: 1 / τ _F = πδf. The filter suppresses noise, but leaves any interference in the vicinity of k = 0 in the local frequency space almost unaffected. Such disturbances - for example due to extrapolation errors or signal distortion - would lead to low-frequency image amplitude variations, even where there is no signal contribution from the examination object (see FIG. 1). The fact that the image amplitude values in the signal-free areas continue to strive towards zero after application of the filter shows that reconstruction errors can be neglected. The structures just barely recognizable at the edge of the area shown are also present in the following profiles in FIGS. 9-11 at higher band widths Δf _B in the same form. They can be traced back to the finite number of projections. The fluctuation of the extrapolated values for S (0), which was determined using the method of linear prediction using the first L = 128 data points and J = 32 coefficients, is 2% based on their mean value.
• 9. In FIG. 9, profiles of the above-mentioned sample tube with NaCl solution for Δf _B = 125.0 kHz and an acquisition time of T = 1024 μs per induction signal are shown. The fluctuation of the extrapolated values for S (0), which was determined using the linear prediction method using the first L = 64 data points and J = 16 coefficients, is 2% based on their mean value. The description of FIG. 8 apply accordingly.
• 10. In FIG. 10, profiles of the above-mentioned sample tube with NaCl solution for Δf _B = 250.0 kHz and an acquisition time of T = 512 μs per induction signal are shown. The fluctuation of the extrapolated values for S (0), which was determined using the method of linear prediction using the first L = 32 data points and J = 8 coefficients, is 5% based on their mean value. The description of FIG. 8 apply accordingly.
• 11. In FIG. 11, profiles of the above-mentioned sample tube with NaCl solution for Δf _B = 333.3 kHz and an acquisition time of T = 384 μs per induction signal are shown. The fluctuation of the extrapolated values for S (0), which was determined using the linear prediction method using the first L = 24 data points and J = 6 coefficients, is 4% based on their mean value. The description of FIG. 8 apply accordingly.
• 12. With Fig. 12, the favorable properties of the invention in relation to susceptibility leaps are to be demonstrated. The air-water limit at the filler neck of a spherical sample bottle is shown. The surface coil used only illuminates a small part of the examination object. You can see the filler neck from above. The two-dimensional variant of the invention was used again. Strong local magnetic field gradients prevail at the air-water boundary, which in the field echo recording (FE) with an echo time of T _E = 2 ms already lead to serious image artifacts and to signal cancellations. In the recording with the method (FID) according to the invention, only a slight misrepresentation without signal extinctions can be recorded. In the two images above, Δf _B = 125 kHz. In the lower three recordings, which were obtained with the method according to the invention (FID), it is demonstrated how the air-water limit is at different signal bandwidths. The bandwidths Δf _B are given below the pictures. The contour is reproduced completely sharply at Δf _B = 250 kHz.
• 13. In FIG. 13 the limitation of the resolution by the relaxation is shown in the method according to the invention. In order to investigate the influence of relaxation on the achievable spatial resolution, a hypothetical (one-dimensional) experiment is considered in which, at time t = 0, broadband high-frequency excitation takes place with the magnetic field gradient G switched on. After a time t = T, the magnetic field gradient is inverted, so that there is a field echo at t = 2T. The field echo and the spin echo pulse sequence behave in the same way with regard to the signal weakening by relaxation. One only has to replace T * | 2 with T ₂ in the case of the spin echo pulse sequence. In the case of the spin echo pulse sequence, a refocusing pulse without inversion of the magnetic field gradient is to be inserted at the point t = T, so that a spin echo is formed at t = 2T. We refer to the field echo and the spin echo pulse sequence here as echo pulse sequences (ECHO), while the method according to the invention is identified as a Fid pulse sequence (FID). With the Fid pulse sequence, we assume two excitations with oppositely polarized magnetic field gradients in order to arrive at the same number of digitization points as with the echo method. . In the upper illustration of Figure 13, the waveform for T * | 2 is shown. For the line width δr and the line height A of an exponentially decaying point source S _λ (η) = exp (-ηλ) with η = t / T and λ = T / T * | 2, the result for amplitude reconstruction for λ »1
  where ζ = fT and denotes the FOURIER transformation. The line width in echo pulse sequences is larger by a factor of √3 than in the Fid pulse sequence due to the asymmetrical signal curve in the spatial frequency domain. However, the signal loss with echo pulse sequences has a far more serious impact: With λ = 1, the signal amplitude with echo pulse sequences is a quarter of the value of the Fid pulse sequence, with λ = 2 the ratio drops to three percent. In the middle illustration in FIG. 13 is the dependence of the line width
  plotted by T for the Fid pulse sequence and echo pulse sequences. Δr _T denotes the line width (without signal decay) for a given acquisition time T per induction signal, δr _{T * | 2} is the line width due to relaxation. The line height for the corresponding pulse sequences is shown in the lower illustration in FIG. 13. The parameters are T * | 2 = 180 µs and G = 91.75 mT / m.
• 14. The limitation of the resolution by the diffusion in the method according to the invention is shown in FIG. 14. To investigate the influence of diffusion on the achievable spatial resolution, the same hypothetical experiment as in FIG. 13 is considered. With regard to the signal attenuation by diffusion, characterized by a diffusion constant D, the field echo and the spin echo pulse sequence also behave in the same way. The signal weakening in the interval [0, 3T] is through
  given, where µ ³ = γ ² G ² T ³ D / 3. This signal curve is shown in the upper illustration in FIG. 14. The depiction of the line width is in the middle illustration in FIG. 14
  from the acquisition time T per induction signal for the Fid pulse sequence and echo pulse sequences for amplitude reconstruction. With δr _T again the line width (without signal decay) is given for a given acquisition time T per induction signal, δr _D is the line width due to the diffusion. In the un direct illustration of FIG. 14 is the line height for the corresponding pulse sequences. The parameters used are D = 2. 10 ^-9 m ² / s and G = 200 mT / m. The achievable spatial resolution is approximately twice as high with the Fid pulse sequence as with the echo method. As can be seen, the line broadening in echo pulse sequences even increases again after a certain measuring time T. The cause lies in the signal maximum at t / T = √2, which is caused by the partial rephasing of those spins that have hardly changed their direction of movement in the time interval [0, T]. The ratio of the signal maximum to the signal amplitude at the echo center
  grows exponentially with diffusion. This increases the asymmetrical amplitude weighting in spatial frequency space, so that the dispersive component of the spectrum gains weight. This is responsible for the increasing line width in the amplitude reconstruction. The signal behavior of the echo pulse sequences makes their optimization more difficult than that of the Fid pulse sequence. In the case of the Fid pulse sequence, the spatial resolution can be reduced by suppressing high spatial spatial frequencies until a satisfactory signal-to-noise ratio is obtained. With echo pulse sequences, this decision must be made before the experiment. If the aim is to achieve a high spatial resolution, the experiment may have to be repeated because the signal-to-noise ratio is too small.

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Claims (10)

1. Magnetic resonance imaging method in which

• a) an examination object, which contains particles with their own angular momentum, is brought into a largely homogeneous magnetic field,
• b) a magnetic field gradient G _m , m = 1 of predetermined amplitude and orientation is applied, which serves as a sequence coding gradient,
• c) a high-frequency excitation pulse is sent, which ends at time t _m , m = 1,
• d) the signal caused by the high-frequency excitation pulse is received at least over a predetermined time T,
• e) this signal is sampled with a scanning bandwidth Δf, n <1 signal values being registered per excitation, the first of which is recorded at a time t _m + τ at a given waiting time τ at the earliest,
• f) the processes (b) - (e) for a predetermined number of M - 1 magnetic field gradients G _m , m = 2,. . . , M be repeated,

characterized by

• a) that for at least one of the M processes (b) - (e) - for example for the m'th - the first signal value is recorded at the time t _{m '} + τ,
• b) that the maximum signal bandwidth Δf _{S of} the examination object under all ver used magnetic field gradients G _m , m = 1,. . . , M by means of the magnetic field gradients G _m , m = 1,. . . , M is set such that τΔf _S <1,
• c) that the scanning bandwidth is selected according to Δf ≧ Δf _S ,

so that the reconstruction error is reduced by missing contributions of unmeasured signal values in the time domain of the high-frequency excitation pulses and the waiting time τ following each high-frequency excitation pulse. 2. Magnetic resonance imaging method according to claim 1, characterized in that τΔf _S ≦ 0.8 applies. 3. Magnetic resonance imaging method according to claim 1, characterized in that τΔf _S ≦ 0.5 applies. 4. Magnetic resonance imaging method according to claim 1, characterized in that τΔf _S ≦ 0.25 applies. 5. Magnetic resonance imaging method according to claim 1, characterized in that τΔf _S ≦ 0.125 applies. 6. Magnetic resonance imaging method according to claim 1, characterized in that τΔf _S ≦ 0.05 applies. 7. Magnetic resonance imaging method according to one of the preceding claims characterized, that unmeasured signal values in the temporal range of the high-frequency excitation pulses and the waiting time τ following each high-frequency excitation pulse by an extra Polation or approximation methods can be determined so that the reconstruction error is reduced.   8. Magnetic resonance imaging method according to one of the preceding claims, characterized in
that the signal value corresponding to the volume integral of the signal density ρ
field gradient is determined from the signal of one or more additional excitations when the magnetic field is switched off, so that the reconstruction error is reduced. 9. Magnetic resonance imaging method according to one of the preceding claims, characterized in that the transition from the magnetic field gradient G _m to the magnetic field gradient G _{m + 1} for at least one of the m = 1,. . . , M - 1 already takes place during signal reception. 10. Magnetic resonance imaging method according to one of the preceding claims characterized, that a predetermined gradient and / or high-frequency pulse sequence precedes the measurement is set, or that it is inserted at selected times during the measurement ben, so that the contrast is affected.