A method for magnetic resonance imaging acquires multi-channel subsampled k-space data using multiple receiver coils; performs singular-value-decomposition on the multi-channel subsampled k-space data to produce compressed multi-channel k-space data which normalizes the multi-channel subsampled k-space data; applies a first center block of the compressed multi-channel k-space data as input to a first convolutional neural network to produce a first estimated k-space center block that includes estimates of k-space data missing from the first center block; generates an n-th estimated k-space block by repeatedly applying an (n−1)-th estimated k-space center block combined with an n-th center block of the compressed multi-channel k-space data as input to an n-th convolutional neural network to produce an n-th estimated k-space center block that includes estimates of k-space data missing from the n-th center block; reconstructs image-space data from the n-th estimated k-space block.