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Model-based methods are widely used for reconstruction in compressed sensing(CS) magnetic resonance imaging (MRI), using regularizers to describe theimages of interest. The reconstruction process is equivalent to solving acomposite optimization problem. Accelerated proximal methods (APMs) are verypopular approaches for such problems. This paper proposes a complexquasi-Newton proximal method (CQNPM) for the wavelet and total variation basedCS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations toconverge but needs to compute a more challenging proximal mapping calledweighted proximal mapping (WPM). To make CQNPM more practical, we proposeefficient methods to solve the related WPM. Numerical experiments demonstratethe effectiveness and efficiency of CQNPM.

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