A fast nonconvex Compressed Sensing algorithm for highly low-sampled MR images reconstruction

TL;DR

This paper introduces a fast, efficient non-convex compressed sensing algorithm for reconstructing highly under-sampled MRI images, demonstrating superior performance and computational efficiency over existing methods.

Contribution

The paper proposes the FNCR algorithm, a novel iterative method that linearizes non-convex problems and employs advanced strategies for efficient MRI reconstruction from sparse data.

Findings

High-quality MRI reconstruction from severely under-sampled data

Faster convergence and computational efficiency compared to existing methods

Effective handling of non-convex regularization in compressed sensing

Abstract

In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained minimization problem with a family of non-convex regularizing objective functions depending on a parameter and a least squares data fit constraint. We propose a fast and efficient algorithm, named Fast NonConvex Reweighting (FNCR) algorithm, based on an iterative scheme where the non-convex problem is approximated by its convex linearization and the penalization parameter is automatically updated. The convex problem is solved by a Forward-Backward procedure, where the Backward step is performed by a Split Bregman strategy. Moreover, we propose a new efficient iterative solver for the arising linear systems. We prove the convergence of the proposed FNCR method. The results on synthetic phantoms and real images show that the algorithm is very well performing and computationally efficient, even when compared to the best performing methods proposed in the literature.