Randomized dimension reduction for magnetic resonance image iterative reconstruction
In a method for magnetic resonance imaging pseudorandomly undersampled k-space imaging data is acquired with multiple receiver coils of an MRI imaging apparatus. MR image reconstruction is performed to produce a reconstructed MR image from the k-space imaging data by iteratively solving sketched approximations of an original reconstruction problem. The sketched approximations use a sketched model matrix A s that is a lower-dimensional version of an original model matrix A of the original reconstruction problem. The sketched model matrix A s preserves the Fourier structure of the MR reconstruction problem and reduces the number of coils actively used during reconstruction.
1. A method for magnetic resonance imaging comprising:
acquiring with multiple receiver coils of an MRI imaging apparatus pseudorandomly undersampled k-space imaging data;
performing MR image reconstruction to produce a reconstructed MR image from the pseudorandomly undersampled k-space imaging data;
wherein the reconstruction comprises iteratively solving sketched approximations of an original reconstruction problem, wherein the sketched approximations use a sketched model matrix A s that is a lower-dimensional version of an original model matrix A of the original reconstruction problem;
wherein the sketched model matrix A s preserves the Fourier structure of the MR reconstruction problem and reduces the number of coils actively used during reconstruction.
2. The method of claim 1 wherein the pseudorandomly undersampled k-space imaging data have both spatial and temporal dimensions.
3. The method of claim 1 wherein iteratively solving the sketched approximations of the original reconstruction problem comprises iteratively solving second-order Taylor approximations with a sketched Hessian that includes the sketched model matrix A s .
4. The method of claim 1 wherein the sketched model matrix A s is related to the original model matrix A by A t s =S t A, where S is a structured sketching matrix.
5. The method of claim 4 wherein the structured sketching matrix S is the product of two matrices S PCA and S R , where S PCA estimates virtual coils from principal components and S R sketches the virtual coils.
6. The method of claim 5 wherein S R sketches a reduced number of high-energy virtual coils and also includes random linear combinations of remaining low-energy coils.
7. The method of claim 5 wherein multiplication of S PCA by a coil sensitivity map operator C produces a sensitivity map operator C PCA with virtual coils sorted according to descending energy.