Method for reconstructing a motion-corrected magnetic resonance image of a subject

1. A method for reconstructing a motion-corrected magnetic resonance image of a subject, the method comprising:

providing k-space magnetic resonance data comprising a plurality of shots, wherein each shot of the plurality of shots corresponds to an individual motion state of the subject;

providing motion parameters related to each individual motion state of a plurality of motion states;

determining redundancies across the plurality of motion states of the plurality of shots based on the motion parameters, wherein the redundancies across the plurality of motion states are determined by finding similarities between different motion states, and wherein the finding of the similarities comprises comparing the motion parameters of the different motion states with each other and finding a redundancy when differences between the different motion states are below a predetermined threshold;

compressing the plurality of motion states based on the determined redundancies across the plurality of motion states; and

reconstructing a magnetic resonance image from the k-space magnetic resonance data based on the compressed plurality of motion states.

2. The method of claim 1 , wherein the compressing of the plurality of motion states comprises forming groups of motion states such that each group of motion states contains motion states that are similar to each other with respect to the respective motion parameters.

3. The method of claim 2 , wherein the forming of the groups of motion states comprises comparing the motion parameters of different shots of the plurality of shots with each other.

4. The method of claim 3 , wherein the comparing of the motion parameters comprises comparing all of the shots of the plurality of shots with each other.

5. The method of claim 2 , wherein new common motion parameters are assigned to each group of similar motion states,

wherein the new common motion parameters are within a range of original motion parameters of the motion states of a respective group, and

wherein the new common motion parameters are a mean of the original motion parameters of the motion states of the respective group.

6. The method of claim 1 , wherein every motion parameter of the motion parameters comprises at a plurality of components, and

wherein a group of motion states are categorized to be similar to each other when every component of the motion parameter of any motion state of the group of motion states differs no more than a predetermined threshold value from corresponding components of the motion parameter of any other motion state of the group of motion states.

7. The method of claim 1 , wherein the motion parameters are determined via a retrospective motion correction method, via a motion tracking device, via a navigator method, or a combination thereof.

8. A method for reconstructing a motion-corrected magnetic resonance image of a subject, the method comprising:

providing k-space magnetic resonance data comprising a plurality of shots, wherein each shot of the plurality of shots corresponds to an individual motion state of the subject;

providing motion parameters related to each individual motion state of a plurality of motion states;

determining redundancies across the plurality of motion states of the plurality of shots based on the motion parameters;

compressing the plurality of motion states based on the determined redundancies across the plurality of motion states; and

reconstructing a magnetic resonance image from the k-space magnetic resonance data based on the compressed plurality of motion states,

wherein the magnetic resonance image is reconstructed by minimizing a data consistency error between the provided k-space data and a forward model described by an encoding operator, and

wherein the encoding operator comprises the motion parameters for each shot of the plurality of shots, Fourier encoding, and optionally subsampling and coil sensitivities of a multi-channel coil array.

9. A method for reconstructing a motion-corrected magnetic resonance image of a subject, the method comprising:

providing k-space magnetic resonance data comprising a plurality of shots, wherein each shot of the plurality of shots corresponds to an individual motion state of the subject;

providing motion parameters related to each individual motion state of a plurality of motion states;

providing a magnetic resonance reference image of the subject;

determining redundancies across the plurality of motion states of the plurality of shots based on the magnetic resonance reference image and the motion parameters;

compressing the plurality of motion states based on the determined redundancies across the plurality of motion states; and

reconstructing a magnetic resonance image from the k-space magnetic resonance data based on the compressed plurality of motion states.

10. The method of claim 9 , wherein the magnetic resonance reference image is a low-resolution image having a spatial resolution in a range of 2-8 mm in a phase encode plane.

11. The method of claim 9 , wherein motion images are computed by rotating and/or translating the magnetic resonance reference image using the motion parameters and/or by applying motion vector fields relating to the motion states, to obtain a motion image for each shot of the plurality of shots, and

wherein the determining of the redundancies is based on the motion images.

12. The method of claim 11 , wherein singular values and a compression matrix are determined by applying a singular value decomposition to the motion images from each shot of the plurality of shots,

wherein the compression matrix is a V matrix from the singular value decomposition, and

wherein the compression matrix is truncated after the singular value decomposition.

13. The method of claim 12 , wherein the truncating of the compression matrix is based on a decay of the singular values.

14. The method of claim 12 , wherein the magnetic resonance image is reconstructed via a SENSE+motion model that is at least modified by the truncated compression matrix.

15. A non-transitory computer program comprising instructions, wherein, when the computer program is executed by a data processing device, the data processing device is configured to:

provide k-space magnetic resonance data comprising a plurality of shots, wherein each shot of the plurality of shots corresponds to an individual motion state of a subject;

provide motion parameters related to each individual motion state of a plurality of motion states;

provide a magnetic resonance reference image of the subject;

determine redundancies across the plurality of motion states of the plurality of shots based on the magnetic resonance reference image and the motion parameters;

compress the plurality of motion states based on the determined redundancies across the plurality of motion states; and

reconstruct a magnetic resonance image from the k-space magnetic resonance data based on the compressed plurality of motion states.

16. A data processing device comprising:

a processor configured to:

provide k-space magnetic resonance data comprising a plurality of shots, wherein each shot of the plurality of shots corresponds to an individual motion state of a subject;

provide motion parameters related to each individual motion state of a plurality of motion states;

provide a magnetic resonance reference image of the subject;

determine redundancies across the plurality of motion states of the plurality of shots based on the magnetic resonance reference image and the motion parameters;

compress the plurality of motion states based on the determined redundancies across the plurality of motion states; and

reconstruct a magnetic resonance image from the k-space magnetic resonance data based on the compressed plurality of motion states.