2-D learned proximal gradient algorithm for fast sparse matrix recovery

Many real-world problems can be modeled as sparse matrix recovery from two-dimensional (2D) measurements, which is recognized as one of the most important topics in signal processing community. Benefited from the roaring success of compressed sensing, many classical iterative algorithms can be directly applied or reinvented for matrix recovery, though they are computationally expensive. To alleviate this, we propose a neural network named 2D learned proximal gradient algorithm (2D-LPGA), which aims to quickly reconstruct the target matrix. Theoretical analysis reveals that if the parameters of the network satisfy certain conditions, it can reconstruct the sparse signal with linear convergence rate. Moreover, numerical experiments demonstrate the superiority of the proposed method over other classical schemes.