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.
@article{arxiv.2303.02586,
title = {A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI},
author = {Tao Hong and Luis Hernandez-Garcia and Jeffrey A. Fessler},
journal= {arXiv preprint arXiv:2303.02586},
year = {2024}
}