Compressive sensing method for improved reconstruction of gradient-sparse magnetic resonance images

We propose a compressive sensing method for reconstructing gradient-sparse magnetic resonance (MR) images based on the pre-filtering of the input signals in the k-space. A set of filtered versions of the image is reconstructed using the available k-space samples, and a final reconstruction stage generates the desired image from the filtered versions. Our experiments, conducted over real MR images and angiograms, show that the proposed method improves the reconstruction over the total-variation minimization, in terms of signal-to-noise ratio and computation time. The proposed method is particularly appropriate for computing MR angiograms, which are typically sparse under the finite-differences operation.