Multi-contrast MRI image reconstruction using machine learning

1. A computer-implemented method for reconstructing a MRI image, comprising:

receiving a plurality of MRI measurement data sets ƒ 1 to ƒ N , wherein each data set is acquired from an examination object based on a different MRI protocol of an MRI system;

receiving MRI images u 1 0 to u N 0 corresponding to the MRI measurement data sets ƒ 1 to ƒ N ;

applying, in at least a first step GD 1 , trained functions to the MRI images u 1 0 to u N 0 , using a neural network and a forward-sampling operator, wherein at least one output MRI image u T is generated; and

providing the at least one output MRI image u T ,

wherein the forward-sampling operator determines an agreement between at least one MRI image u 1 0 to u N 0 and the corresponding MRI measurement data set ƒ 1 to ƒ N .

2. The computer-implemented method according to claim 1 , wherein applying trained functions to the MRI images u 1 0 to u N 0 comprises:

applying a variational model to the MRI images u 1 0 to u N 0 , wherein, for each input MRI image u 1 0 to u N 0 , an output of the neural network and an output of the forward-sampling operator is subtracted from the respective input MRI image u 1 0 to u N 0 .

3. The computer-implemented method according to claim 1 , wherein the neural network is a convolutional neural network, and wherein applying trained functions to the MRI images u 1 0 to u N 0 comprises:

applying a plurality of trained filter functions to the MRI images u 1 0 to u N 0 simultaneously, using convolutions and non-linear activations, wherein each filter function is applied to each MRI image u 1 0 to u N 0 .

4. The computer-implemented method according to claim 1 , wherein, for each of the MRI images u 1 0 to u N 0 separately, the forward-sampling operator determines an agreement between of the MRI image u 1 0 to u N 0 and the corresponding MRI measurement data sets ƒ 1 to ƒ N using a MRI forward model of the corresponding MRI protocol.

5. The computer-implemented method according to claim 1 , further comprising:

receiving coil sensitivities C of the MRI system; and

receiving an under-sampling scheme for each MRI protocol;

wherein the forward-sampling operator determines an agreement between a respective MRI image u 1 0 to u N 0 and the corresponding MRI measurement data set ƒ 1 to ƒ N using a MRI forward model of the MRI protocol, based on the coil sensitivities C and the respective under-sampling scheme.

6. The computer-implemented method according to claim 1 , wherein applying, in at least one step GD 1 , trained functions to the MRI images u 1 0 to u n 0 comprises:

applying, in a plurality of steps GD 1 to GD T for a predefined number T, trained functions to the MRI images u 1 0 to u N 0 , each step GD t for t=1 . . . T comprising:

receiving input MRI images u 1 t−1 to u N t−1 ;

applying trained functions to the MRI images u 1 t−1 to u N t−1 , using the neural network, and the forward-sampling operator, wherein MRI output images u 1 t to u N t are generated; and

providing the MRI output images u i t to u N t .

7. The computer-implemented method according to claim 6 , wherein applying trained functions to the input MRI images u 1 t−1 to u N t−1 comprises:

applying the neural network and the forward-sampling operator on the input MRI images u 1 t−1 to u N t−1 ; and

subtracting, for each input MRI image u 1 t−1 to u N t−1 , an corresponding output of the neural network and output of the forward-sampling operator from the input MRI image u 1 t to u N t .

8. The computer-implemented method according to claim 1 , wherein the forward-sampling operator determines an agreement between each MRI image u i t−1 , with i=0 . . . N, and the corresponding MRI measurement dataset ƒ i , using the relation

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wherein λ i t−1 is a contrast specific regularization parameter, and A i is a MRI forward model for the corresponding MRI protocol.

9. The computer-implemented method according to claim 1 , wherein the MRI measurements data sets ƒ 1 to ƒ N are based on different MRI contrasts of the MRI system.

10. The computer-implemented method according to claim 1 , wherein the MRI measurement data sets ƒ 1 to ƒ N are acquired based on WAVE-CAIPI MRI protocols with different contrasts.

11. The computer-implemented method according to claim 1 , wherein the at least one output MRI image u T is an output image u i T , for i={1 . . . N}, of a plurality of output MRI images u 1 T to u N T , wherein each output MRI image u 1 T to u N T , corresponds to a respective one of the MRI images u 1 0 to u N 0 .

12. The computer-implemented method according to claim 1 , wherein each MRI measurement data set ƒ 1 to ƒ N is undersampled in k-space based on a specific under-sampling scheme.

13. The computer-implemented method according to claim 8 , wherein at least two of the MRI measurement data sets ƒ 1 to ƒ N are based on different under-sampling schemes, specifically on complementary under-sampling schemes.

14. The computer-implemented method according to claim 1 , wherein reconstructing MRI images u 1 0 to u N 0 from the MRI measurement data sets ƒ 1 to ƒ N further comprises:

removing a low-resolution background phase from the MRI images u 1 0 to u N 0 .

15. The computer-implemented method according to claim 1 , wherein applying trained functions to the MRI images u 1 0 to u N 0 further comprises:

dividing the coil sensitivities C, the MRI measurement data sets ƒ 1 to ƒ N , the MRI images u 1 0 to u N 0 , and the reference images g 1 to g N into patches of collapsing voxel groups, and

applying the trained functions to the patches of collapsing voxel groups of each MRI image u 1 0 to u N 0 individually.

16. A non-transitory computer-readable storage medium comprising a computer program having instructions which, when executed by a computer, cause the computer to carry out the method of claim 1 .

17. A computer-implemented method for providing trained functions for reconstructing an MRI image, comprising:

receiving a plurality of MRI measurement data sets ƒ 1 to ƒ N , wherein each data set is acquired from an examination object based on a different MRI protocol of an MRI system;

receiving reference MRI images g 1 to g N with reduced MRI artefacts or noise amplification compared to the MRI images u 1 0 to u N 0 , corresponding to the MRI measurement data sets ƒ 1 to ƒ N ;

receiving MRI images u 1 0 to u N 0 corresponding to the MRI measurement data sets ƒ 1 to ƒ N ;

applying, in at least a first step GD 1 , functions to the MRI images u 1 0 to u N 0 using a neural network and a forward-sampling operator, wherein at least one output MRI image u T is generated; and

determining a difference between the at least one output MRI image u T and the corresponding reference image g i , i={1 . . . N};

training the functions based on the determined difference; and

providing the trained functions;

wherein the forward-sampling operator determines an agreement between at least one MRI image u 1 0 to u N 0 and the corresponding MRI measurement data set ƒ 1 to ƒ N .

18. A computer configured for reconstructing an MRI image, the computer having a memory, an interface, and at least one processor, the memory storing instructions executable by said at least one processor, wherein execution of the instructions causes the computer to:

receive, by the interface, a plurality of MRI measurement data sets ƒ 1 to ƒ N , wherein each data set is acquired from an examination object based on a different MRI protocol of a MRI system;

receive, by the interface, MRI images u 1 0 to u N 0 corresponding to the MRI measurement data sets ƒ 1 to ƒ N ;

apply, by the processor, in at least a first step GD 1 , trained functions to the MRI images u 1 0 to u N 0 , using a neural network and a forward-sampling operator based on a MRI forward model, wherein at least one output MRI image u i T is generated; and

provide, by the interface, the at least one output MRI image u T ,

wherein the forward-sampling operator determines an agreement between at least one MRI image u 1 0 to u N 0 and the corresponding MRI measurement data set ƒ 1 to ƒ N .

19. The computer according to claim 18 , wherein execution of the instructions further causes the computer to:

receive reference MRI images g 1 to g N with reduced MRI artefacts or noise amplification compared to the MRI images u 1 0 to u N 0 , corresponding to the MRI measurement data sets ƒ 1 to ƒ N ;

determine a difference between the at least one output MRI image u T and the corresponding reference image g i , i={1 . . . N};

train the functions based on the determined difference; and

provide the trained functions.

20. An MRI system comprising at least one computer according to claim 18 .