A Novel Model for Compressed Sensing MRI via Smoothed ℓ1-Norm Regularization

Abstract

Compressed sensing magnetic resonance imaging (CS-MRI) using ℓ1-norm minimization has been widely and successfully applied. However, ℓ1-norm minimization often leads to bias estimation and the solution is not as accurate as desired. In this paper, we propose a novel model for MR image reconstruction, which takes as a smoothed ℓ1-norm regularization model that is convex, has a unique solution. More specifically, we employ the logarithm function with the parameter in our optimization, and an iteration technique is developed to solve the proposed minimization problem for MR image reconstruction efficiently. The model is simple and effective in the solution procedure. Simulation results on normal brain image demonstrated that the performance of the proposed method was better than some traditional methods.