Method of improved multiple-phase dynamic contrast-enhanced magnetic resonance imaging with motion correction using water/fat signal separation

Abstract

A method of operating a magnetic resonance imaging system (10) with regard to acquiring multiple-phase dynamic contrast-enhanced magnetic resonance images, the method comprising steps of acquiring (48) a first set of magnetic resonance image data (x.sub.pre) prior to administering a contrast agent to the subject of interest (20), by employing a water/fat magnetic resonance signal separation technique, determining (52) a first image of the spatial distribution of fat (I.sub.pre) of at least the portion of the subject of interest (20), acquiring (50) at least a second set of magnetic resonance image data (x.sub.2) of at least the portion of the subject of interest (20) after administering the contrast agent to the subject of interest (20), by employing a water/fat magnetic resonance signal separation technique, determining (54) at least a second image of the spatial distribution of fat (I.sub.2.sup.ph) of at least the portion of the subject of interest (20), applying (56) an image registration method to the second image of the spatial distribution of fat (I.sub.2.sup.ph) with reference to the first image of the spatial distribution of fat (I.sub.pre) for correcting a potential motion of the subject of interest (20); and a magnetic resonance imaging system (10) having a control unit (26) that is configured to carry out steps (56-64) of such a method; and a software module (44) for carrying out such a method, wherein the method steps (56-64) to be conducted are converted into a program code that is implementable in a memory unit (30) and is executable by a processor unit (32) of the magnetic resonance imaging system (10).

Claims

1. A method of operating a magnetic resonance imaging system with regard to acquiring multiple-phase dynamic contrast-enhanced magnetic resonance images, the magnetic resonance imaging system being configured for acquiring magnetic resonance images of at least a portion of a subject of interest, the method comprising: acquiring a first set of magnetic resonance image data (xpre) of the at least a portion of the subject of interest prior to administering a contrast agent to the subject of interest; determining a first image of a spatial distribution of fat (Ipre) of the at least a portion of the subject of interest from the first set of magnetic resonance image data (xpre) using a water/fat magnetic resonance signal separation technique; acquiring a plurality of additional sets magnetic resonance image data (xi) of the at least a portion of the subject of interest after administering the contrast agent to the subject of interest; determining a plurality of images of the spatial distribution of fat (Iiph) of the at least a portion of the subject of interest from the plurality of additional sets of magnetic resonance image data (xi) using the water/fat magnetic resonance signal separation technique; applying an image registration method to each of the plurality of images of the spatial distribution of fat (Iiph) with reference to the first image of the spatial distribution of fat (Ipre) to determine transformations for minimizing differences between the plurality of images of the spatial distribution of fat (Iiph) and the first image of the spatial distribution of fat (Ipre); and applying the determined transformations to the plurality of additional sets of magnetic resonance image data (xi) for correcting for motion of the subject of interest in magnetic resonance images reconstructed from the additional sets of magnetic resonance image data (xi), respectively, the motion having occurred in times between acquiring the first set of magnetic resonance image data (xpre) and acquiring the additional sets of magnetic resonance image data (xi).

2. The method of claim 1 wherein the water/fat magnetic resonance signal separation technique is based on a difference in Larmor frequencies of excited nuclei due to chemical shift.

3. The method of claim 1, wherein the additional sets of magnetic resonance image data (xi) acquired after administering the contrast agent are obtained using a compressed sensing method.

4. The method of claim 1, further comprising applying a filter to the first set of magnetic resonance image data (xpre) acquired prior to administering the contrast agent to the subject of interest, wherein the filter is equivalent to a high pass filter in k-space.

5. A magnetic resonance imaging system configured for acquiring magnetic resonance images of at least a portion of a subject of interest, comprising: an examination space configured for positioning the at least a portion of the subject of interest within; a main magnet configured for generating a static magnetic field in the examination space; a magnetic gradient coil system configured for generating gradient magnetic fields superimposed to the static magnetic field; at least one transmitting radio frequency antenna device configured for applying a radio frequency excitation field to nuclei of or within the at least a portion of the subject of interest for magnetic resonance excitation; at least one receiving radio frequency antenna device configured for receiving magnetic resonance signals from the nuclei of or within the portion of the subject of interest that have been excited by applying the radio frequency excitation field; a controller, comprising memory and at least one processor, configured for controlling functions of the magnetic resonance imaging system, wherein the memory stores instructions that, when executed by the at least one processor, cause the at least one processor to perform a process comprising: receiving a first set of magnetic resonance image data (xpre) of the at least a portion of the subject of interest acquired prior to administering a contrast agent to the subject of interest; determining a first image of a spatial distribution of fat (Ipre) of the at least a portion of the subject of interest from the first set of magnetic resonance image data (xpre) using a water/fat magnetic resonance signal separation technique; receiving a plurality of additional sets of magnetic resonance image data (xi) of the at least a portion of the subject of interest acquired after administering the contrast agent to the subject of interest; determining a plurality of images of the spatial distribution of fat (Iiph) of the at least a portion of the subject of interest from the plurality of additional sets of magnetic resonance image data (xi) using the water/fat magnetic resonance signal separation technique; applying an image registration method to each of the plurality of images of the spatial distribution of fat (Iiph) with reference to the first image of the spatial distribution of fat (Ipre) to determine transformations for minimizing differences between the plurality of images of the spatial distribution of fat (Iiph) and the first image of the spatial distribution of fat (Ipre); and applying the determined transformations to the received plurality of additional sets of magnetic resonance image data (xi) for correcting for motion of the subject of interest in magnetic resonance images reconstructed from the additional sets of magnetic resonance image data (xi), respectively, the motion having occurred in times between acquiring the first set of magnetic resonance image data (xpre) and acquiring the additional sets of magnetic resonance image data (xi).

6. The system of claim 5, wherein the water/fat magnetic resonance signal separation technique is based on a difference in Larmor frequencies of excited nuclei due to chemical shift.

7. The system of claim 5, wherein the additional sets of magnetic resonance image data (xi) acquired after administering the contrast agent are obtained using a compressed sensing method.

8. The system of claim 5, wherein the process performed by the at least one processor further comprises: applying a filter to the first set of magnetic resonance image data (xpre) acquired prior to administering the contrast agent to the subject of interest, wherein the filter is equivalent to a high pass filter in k-space.

9. A non-transitory computer readable medium storing instructions for controlling acquisition of multiple-phase dynamic contrast-enhanced magnetic resonance images of at least a portion of a subject of interest, the instructions, when executed by a computer processor, causing the computer processor to perform a method comprising: receiving a first set of magnetic resonance image data (xpre) of the at least a portion of the subject of interest acquired prior to administering a contrast agent to the subject of interest; determining a first image of a spatial distribution of fat (Ipre) of the at least a portion of the subject of interest from the first set of magnetic resonance image data (xpre) using a water/fat magnetic resonance signal separation technique; receiving a plurality of additional sets of magnetic resonance image data (xi) of the at least a portion of the subject of interest acquired after administering the contrast agent to the subject of interest; determining a plurality of images of the spatial distribution of fat (Iiph) of the at least a portion of the subject of interest from the plurality of additional sets of magnetic resonance image data (xi) using the water/fat magnetic resonance signal separation technique; applying an image registration method to each of the plurality of images of the spatial distribution of fat (Iiph) with reference to the first image of the spatial distribution of fat (Ipre) to determine transformations for minimizing differences between the plurality of images of the spatial distribution of fat (Iiph) and the first image of the spatial distribution of fat (Ipre); and applying the determined transformations to the received plurality of additional sets of magnetic resonance image data (xi) to correct for motion of the subject of interest in magnetic resonance images reconstructed from the additional sets of magnetic resonance image data (xi), respectively, the motion having occurred in times between acquiring the first set of magnetic resonance image data (xpre) and acquiring the additional sets of magnetic resonance image data (xi).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. Such embodiment does not necessarily represent the full scope of the invention, however, and reference is made therefore to the claims and herein for interpreting the scope of the invention.

(2) In the drawings:

(3) FIG. 1 is a schematic illustration of a part of an embodiment of a magnetic resonance imaging system in accordance with the invention, and

(4) FIG. 2 shows a flowchart of a method in accordance with the invention of operating the magnetic resonance imaging system pursuant to FIG. 1.

DETAILED DESCRIPTION OF EMBODIMENTS

(5) FIG. 1 shows a schematic illustration of a part of an embodiment of a magnetic resonance imaging system 10 configured for acquiring magnetic resonance images of at least a portion of a subject of interest 20, usually a patient. The magnetic resonance imaging system 10 comprises a scanning unit 12 having a main magnet 14. The main magnet 14 has a central bore that provides an examination space 16 around a center axis 18 for the subject of interest 20 to be positioned within, and is further provided for generating a static magnetic field B.sub.0 at least in the examination space 16. For clarity reasons, a customary table for supporting the subject of interest 20 has been omitted in FIG. 1. The static magnetic field B.sub.0 defines an axial direction of the examination space 16, aligned in parallel to the center axis 18. It is appreciated that the invention is also applicable to any other type of magnetic resonance imaging systems providing an examination region within a static magnetic field.

(6) Further, the magnetic resonance imaging system 10 comprises a magnetic gradient coil system 22 provided for generating gradient magnetic fields superimposed to the static magnetic field B.sub.0. The magnetic gradient coil system 22 is concentrically arranged within the bore of the main magnet 14.

(7) The magnetic resonance imaging system 10 comprises a control unit 26 configured to control functions of the magnetic resonance imaging system 10. The control unit 26 includes a human interface device 24 including a monitor unit having a touch-sensitive screen.

(8) Furthermore, the magnetic resonance imaging system 10 includes a radio frequency antenna device 36 designed as a whole-body coil that is provided for applying a radio frequency excitation field B.sub.1 to nuclei of or within the subject of interest 20 for magnetic resonance excitation during radio frequency transmit time periods to excite the nuclei of or within the subject of interest 20 for the purpose of magnetic resonance imaging. To this end, radio frequency power is fed, controlled by the control unit 26, from a radio frequency transmitter 40 to the whole-body coil. The whole-body coil has a center axis and, in the operational state, is arranged concentrically within the bore of the main magnet 14 such that the center axis of the whole-body coil and the center axis 18 of the scanning unit 12 coincide. As is well known in the art, a cylindrical metal radio frequency shield 34 is arranged concentrically between the magnetic gradient coil system 22 and the whole-body coil.

(9) Moreover, the magnetic resonance imaging system 10 comprises a plurality of radio frequency antenna devices 38 provided for receiving magnetic resonance signals from the nuclei of or within the subject of interest 20 that have been excited by applying the radio frequency excitation field B.sub.1. The radio frequency antenna devices 38 of the plurality of radio frequency antenna devices 38 are designed as an array of local coils that are intended to be positioned proximal to a region of the subject of interest 20 to be imaged, namely the liver. The local coils are configured for receiving magnetic resonance signals from the excited nuclei of or within the portion of the subject of interest 20 to be imaged during radio frequency receiving time periods which are distinct from the radio frequency transmit time periods.

(10) Furthermore, the magnetic resonance imaging system 10 comprises an image processing unit 32 provided for processing magnetic resonance signals to determine magnetic resonance images of at least the portion of the subject of interest 20 from the received magnetic resonance signals.

(11) The magnetic resonance imaging system 10 further comprises a respiration monitoring device 42. The respiration monitoring device 42 includes a respiration sensor that, in an operational state, is attached to the thorax of the subject of interest 20 and is held by a belt which is wound around the thorax. It is appreciated by the one skilled in the art that other types of respiration monitoring devices are as well employable. The respiration monitoring device 42 is configured to provide the control unit 26 with an output signal whose level represents a respiration state of the subject of interest 20. To this end, an output line of the respiration monitoring device 42 is connected to the control unit 26. The control unit 26 of the magnetic resonance imaging system 10 is configured for receiving an output signal from the respiration monitoring device 42. The output signal is displayed on the monitor unit of the human interface device 24. In this way, a breathing pattern and, in particular, breath-hold periods can be checked by an operator.

(12) Magnetic resonance image acquisition during individual breath-holds is performed using a breath-hold adaptive sampling pattern. As an alternative, a related fast sampling scheme could be employed. In the mentioned adaptive sampling pattern, the spatial resolution of the magnetic resonance image is automatically adapted during image acquisition, and is combined with the output signal of the respiration monitoring device 42 in such a way that the acquisition of the magnetic resonance image is terminated at breathing onset. Premature onset of breathing results in an incomplete set of magnetic resonance image data. The adaptive sampling pattern is designed to ensure incoherence at every instance in time, which enables to apply a compressed sensing reconstruction method.

(13) In the following, an embodiment of a method of operating the magnetic resonance imaging system 10 with regard to acquiring multiple-phase dynamic contrast-enhanced magnetic resonance images during breath-hold periods in the respiration of the subject of interest 20 is described. A principal flow chart of the method is given in FIG. 2. In preparation of operating the magnetic resonance imaging system 10, it shall be understood that all involved units and devices are in an operational state and configured as illustrated in FIG. 1.

(14) In order to be able to carry out the method as a specific operation of the magnetic resonance imaging system 10, the control unit 26 comprises a software module 44 (FIG. 1). The method steps to be conducted are converted into a program code of the software module 44, wherein the program code is implementable in a memory unit 28 of the control unit 26 and is executable by a processor unit 30 of the control unit 26.

(15) In a preparatory step 46, via the touch-sensitive screen of the human interface device 24, the operator selects a transversal plane of the portion of the subject of interest 20 to be imaged and the number of phases to be imaged from the portion of the subject of interest 20 before and after administering a contrast agent. In a preceding preparatory calibration measurement, threshold signal levels of the output signal of the respiration monitoring device 42 which correspond to a respiration breath-hold at full inspiration of the subject of interest 20 have been determined. A minimum value of the threshold signal level is stored in the memory unit 28 of the control unit 26.

(16) In a first step 48 of the method, prior to administering the contrast agent to the subject of interest 20, a first set of magnetic resonance image data x.sub.pre is acquired during a breath-hold period in the respiration of the subject of interest 20 at two different echo times.

(17) From the acquired first set of magnetic resonance image data x.sub.pre, a first image of the spatial distribution of fat I.sub.pre of at least the portion of the subject of interest 20 is determined in another step 50 from a full image reconstruction, by employing a water/fat magnetic resonance signal separation technique that is based on the Dixon method, wherein magnetic resonance image data are acquired at one echo time or more than one different echo times. In this particular embodiment, the first set of magnetic resonance image data x.sub.pre is acquired at two different echo times. The Dixon method, well known in the art, is based on the difference in the Larmor frequencies of excited nuclei, in this embodiment given by protons, due to chemical shift.

(18) In the next step then, a gadolinium-based contrast agent is administered to the subject of interest 20 as an intravenous bolus injection.

(19) In another step 52 of the method, after administering the contrast agent to the subject of interest 20, a second set of magnetic resonance image data x.sub.2 of at least the portion of the subject of interest 20 is acquired in the arterial phase and during another breath-hold period in the respiration of the subject of interest 20, wherein the second set of magnetic resonance image data x2 is acquired at two (alternatively three) different echo times.

(20) From the acquired second set of magnetic resonance image data x.sub.2, a second image of the spatial distribution of fat I.sub.2.sup.ph of at least the portion of the subject of interest 20 is determined in another step 54 from an iterative image reconstruction using the water/fat magnetic resonance signal separation technique based on the Dixon method, as will be described later on.

(21) In contrast to the excited protons bound in water, the magnetic resonance image signal stemming from the excited protons bound in the fat tissue of at least a portion of the subject of interest 20 is not affected by the administered contrast agent. Therefore, the image of the spatial distribution of fat I.sub.pre obtained from the first set of magnetic resonance image data x.sub.pre and the image of the spatial distribution of fat I.sub.2.sup.ph obtained from the second set of magnetic resonance image data x.sub.2 are substantially congruent, and a transformation function D.sub.ph.sup.21 exists that minimizes a difference between the first image of the spatial distribution of fat I.sub.pre and the second image of the spatial distribution of fat I.sub.2.sup.ph. The difference is understood with regard to a suitable, specified mathematical norm.

(22) The control unit 26 of the magnetic resonance imaging system 10 includes a rigid-type image registration using software residing in the memory unit 28 of the control unit 26 and being executable by the processor unit 30 of the control unit 26. By applying the image registration method to the second image of the spatial distribution of fat I.sub.2.sup.ph with reference to the first image of the spatial distribution of fat I.sub.pre via the control unit 26 in a next step 56 of the method, the transformation D.sub.21.sup.ph is determined.

(23) Then, in a following step 58 of the method, the determined transformation D.sub.21.sup.ph is applied to the acquired second set of magnetic resonance image data x.sub.2 for correcting a potential motion of the subject of interest 20 having occurred in the time between acquiring the first set of magnetic resonance image data x.sub.pre and the second set of magnetic resonance image data x.sub.2.

(24) In the phase after administering the contrast agent to the subject of interest 20, much narrower time constraints for image reconstruction exist than before administering the contrast agent. In a following step 60 of the method, the determined first image of the spatial distribution of fat I.sub.pre is used as prior knowledge for applying image reconstruction to the second set of magnetic resonance image data x.sub.2 which has been acquired after administering the contrast agent.

(25) The second set of magnetic resonance image data x.sub.2 is thereby obtained by employing parallel imaging or a compressed sensing method for image reconstruction, wherein prior knowledge is given by the existing determined first image of the spatial distribution of fat I.sub.pre, which allows for potential higher under-sampling for the magnetic resonance images to be acquired after administering the contrast agent.

(26) In the same manner as described above, a third set of magnetic resonance image data x.sub.3 is acquired in the portal venous phase and during another breath-hold period in the respiration of the subject of interest 20, wherein magnetic resonance data are acquired at two (alternatively three) different echo times.

(27) The third set of magnetic resonance image data x.sub.3 is obtained by employing parallel imaging or the method of compressed sensing for image reconstruction, wherein the already existing starting basis, given by the determined first image of the spatial distribution of fat I.sub.pre, again allows applying the under-sampling method as described before.

(28) From the acquired third set of magnetic resonance image data x.sub.3, a third image of the spatial distribution of fat I.sub.3.sup.ph of at least the portion of the subject of interest 20 is determined using the water/fat magnetic resonance signal separation technique based on the Dixon method.

(29) By applying the image registration method to the third image of the spatial distribution of fat I.sub.3.sup.ph with reference to the first image of the spatial distribution of fat I.sub.pre via the control unit 26, a transformation D.sub.31.sup.ph is obtained.

(30) Then, the determined transformation D.sub.31.sup.ph is applied to the acquired third set of magnetic resonance image data x.sub.3 for correcting a potential motion of the subject of interest 20 having occurred in the time between acquiring the second magnetic resonance image x.sub.2 and the third magnetic resonance image x.sub.3.

(31) In the above-described manner, also a fourth set and a fifth set of magnetic resonance image data x.sub.4, x.sub.5 of at least the portion of the subject of interest 20 are acquired in the delayed venous phase and in the phase of equilibrium, respectively, during other breath-hold periods in the respiration of the subject of interest 20, wherein the magnetic resonance data are acquired at two (alternatively three) different echo times.

(32) The fourth and the fifth set of magnetic resonance image data x.sub.4, x.sub.5 are obtained by employing the method of compressed sensing for image reconstruction, with the determined first image of the spatial distribution of fat I.sub.pre as starting basis, and by applying the under-sampling method as described above.

(33) From the acquired fourth and fifth set of magnetic resonance image data x.sub.4, x.sub.5, respectively, a fourth image of the spatial distribution of fat I.sub.r.sup.ph and a fifth image of the spatial distribution of fat I.sub.5.sup.ph of at least the portion of the subject of interest 20 are determined using the water/fat magnetic resonance signal separation technique based on the Dixon method.

(34) Transformations D.sub.41.sup.ph and D.sub.51.sup.ph are determined by applying the image registration method to the fourth image of the spatial distribution of fat I.sub.4.sup.ph and the fifth image of the spatial distribution of fat I.sub.5.sup.ph, respectively, with reference to the first image of the spatial distribution of fat I.sub.pre, via the control unit.

(35) In an alternative approach, the second to fifth set of magnetic resonance image data x.sub.2 to x.sub.5 acquired after administering the contrast agent to the subject of interest 20 are commonly obtained by employing a compressed sensing method for image reconstruction, wherein

(36) the determined first image of the spatial distribution of fat I.sub.pre is employed as prior knowledge for reconstruction, and

(37) an affine motion of the subject of interest 20 is involved for applying the registration method to the second to fifth image of the spatial distribution of fat I.sub.2.sup.ph to I.sub.5.sup.ph.

(38) By using the a priori-knowledge about the fat distribution being common to all spatial distributions of fat, and the a priori knowledge that the images of the spatial distribution of fat I.sub.pre, I.sub.2.sup.ph to I.sub.5.sup.ph are associated by a smooth motion of the very same patient, an improved accuracy for image reconstruction can be accomplished and under-sampling artifacts can at least be reduced or potentially prevented.

(39) Another approach for the image reconstruction from acquired magnetic resonance data can be described as an optimization of the following mathematical expression, to be executed for all numbers of index i, indicating the temporal phase,
min|ψx.sub.i|.sub.1+λ.sub.1|UFx.sub.i−y.sub.i|.sub.2+λ.sub.2|I.sub.pre−D.sub.i1.sup.phI.sub.i.sup.ph|.sub.2+λ.sub.3|HF(D.sup.−1.sub.i1.sup.phx.sub.pre)−H(y.sub.i)|.sub.2
with the following denotation:
x.sub.pre set of magnetic resonance image data acquired before administering contrast agent

(40) (first set)

(41) x.sub.i i-th set of magnetic resonance image data acquired after administering contrast agent

(42) y.sub.i k-space data representation of x.sub.i

(43) ψ sparsifying transformation of compressed sensing method

(44) U under-sampling operator

(45) Fourier transform operator

(46) H high pass filter adapted to applicable domain, preferably represented by k-space mathematical p-norm

(47) | |.sub.p mathematical p-norm

(48) λ.sub.1-λ.sub.3 regularization parameters (real numbers)

(49) The first term enforces sparsity of the acquired image in an adequate transform domain.

(50) The second term of the expression ensures data consistency at locations in k-space that were acquired.

(51) The third term of the expression considers the potential motion of the subject of interest 20, occurring between a point in time of acquiring the first set of magnetic resonance image data x.sub.pre, and a point in time of acquiring the i-th set of magnetic resonance image data x.sub.i.

(52) The fourth term of the expression reflects similarity of high frequencies in an applicable domain, which is preferably represented by the k-space, from data acquired prior to administering the contrast agent and after administering the contrast agent.

(53) The regularization parameters λ.sub.1, λ.sub.2, λ.sub.3 can be inputted by the operator via the human interface device 24 as weighting factors. At least one of the regularization parameters λ.sub.1, λ.sub.2, λ.sub.3 can be chosen as zero.

(54) It is interesting to note that the concept described in the equation above could also be applied to appropriate subsets of the data with the ability to correct also for potential motion inconsistencies within the individual wash-in/wash-out phase data sets.

(55) While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.

(56) TABLE-US-00001 REFERENCE SYMBOL LIST 10 magnetic resonance imaging system 12 scanning unit 14 main magnet 16 examination space 18 center axis 20 subject of interest 22 magnetic gradient coil system 24 human interface device 26 control unit 28 memory unit 30 processor unit 32 image processing unit 34 metal radio frequency shield 36 radio frequency antenna device (transmitting) 38 plurality of radio frequency antenna devices (receiving) 40 radio frequency transmitter 42 respiration monitoring device 44 software module 46 preparatory step 48 step of acquiring 1.sup.st set of magnetic resonance image data 50 step of determining 1st image of spatial distribution of fat 52 step of of acquiring 2.sup.nd set of magnetic resonance image data 54 step of determining 2.sup.nd image of spatial distribution of fat 56 step of applying image registration method 58 step of applying determined transformation 60 step of using 1.sup.st image of spatial distribution of fat for image reconstruction B.sub.0 static magnetic field B.sub.1 radio frequency excitation field I.sub.pre 1.sup.st image of spatial distribution of fat I.sub.i.sup.ph i-th image of the spatial distribution of fat x.sub.pre 1.sup.st set of magnetic resonance image data x.sub.i i-th set of magnetic resonance image data