Randomized dimension reduction for magnetic resonance image iterative reconstruction

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 As that is a lower-dimensional version of an original model matrix A of the original reconstruction problem;
• wherein the sketched model matrix As preserves the Fourier structure of the MR reconstruction problem and reduces the number of coils actively used during reconstruction.