Bregman Iteration Based Efficient Algorithm for MR Image Reconstruction From Undersampled K-Space Data

Abstract

It is difficult to solve Magnetic Resonance (MR) image reconstruction problems with linear combinations of total variation and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm regularization terms. In order to solve these compound regularization problems, we propose an efficient algorithm in this letter. The proposed algorithm adopts the Bregman iteration technique to convert the original constrained problem to a sequence of unconstrained problems, which are then solved using operator splitting and variable splitting techniques. Simulation experiments demonstrate that significant improvement of the quality of reconstructed images is achieved by the proposed algorithm when compared to previous methods.