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