Magnetic resonance image reconstruction via Lo-norm minimization

In recent years, Compressed Sensing (CS) has been applied to under-sampling Magnetic Resonance Imaging (MRI) for significantly reducing signal acquisition time. Total Variation (TV), the L1-norm of the discrete gradient-magnitude transform of image, is widely used as the regularization in the CS inspired MRI. Although the classic L1-norm based techniques achieve impressive results, they inherently require a degree of over-sampling to achieve exact reconstruction. In this paper, an iterative algorithm based on the L0-norm is proposed. The proposed method uses the Alternating Direction Method (ADM) to solve the unconstrained Augment Lagrange problem. The problem is first reformulated as the famous Augment Lagrange Function, and then alternatively minimized by ADM. Numerical comparison indicates that the proposed method can obviously improve the reconstruction quality, especially in highly under sample condition.