A magnetic resonance image reconstruction method using support of first-second order variation

This article addresses the problem of reconstructing a magnetic resonance image from highly undersampled data, which frequently arises in accelerated magnetic resonance imaging. We propose to impose sparsity of first and second order difference sparse coefficients within the complement of the known support. Second order variation is involved to overcome blocky effects and support information is used to reduce the sampling rate further. The resulting optimization problem consists of a data fidelity term and first-second order variation terms penalizing entries within the complement of the known support. The efficient split Bregman algorithm is used to solve the problem. Reconstruction results from magnetic resonance imaging data corresponding to different sampling rates are shown to illustrate the performance of the proposed method. Then, we also assess the tolerance of the new method to noise briefly.