A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI

Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest.The reconstruction process is equivalent to solving a composite optimization problem.Accelerated proximal methods (APMs) are very popular approaches for such problems.This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction.Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM).To make CQNPM more practical, we propose efficient methods to solve the related WPM.Numerical experiments on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.