Proximal gradient algorithm with dual momentum for robust compressive sensing MRI

Abstract

Adopting the new signal acquisition technology Compressive Sensing (CS) to Magnetic Resonance Imaging (MRI) reconstruction has been proved to be an effective scheme for reconstruction of high-resolution images with only a small fraction of data, thus making it the key to design a reconstruction algorithm with excellent performance. To achieve accelerated and robust CS-MRI reconstruction, a novel combination of Proximal Gradient (PG) and two types of momentum is developed. Firstly, to accelerate convergence of the PG iteration, we introduce the classical momentum method to solve the data-fitting subproblem for fast gradient search. Secondly, inspired by accelerated gradient strategies for convex optimizations, we further modify the obtained PG algorithm with the Nesterov's momentum technique to solve the prior subproblem, boosting its performance. We demonstrate the effectiveness and flexibility of the proposed method by combining it with two categories of prior models including a weighted nuclear norm regularization and a deep CNN (Convolutional Neural Network) prior model. As such, we obtain a dual momentum-based PG method, which can be equipped with any denoising engine. It is shown that the momentum-based PG method is closely related to the well-known Approximate Message Passing (AMP) algorithm. Experiments validate the effectiveness of leveraging dual momentum to accelerate the algorithm and demonstrate the superior performance of the proposed method both quantitatively and visually as compared with the existing methods.