Deep Unfolding Network for Block-Sparse Signal Recovery

Block-sparse signal recovery has drawn increasing attention in many areas of signal processing, where the goal is to recover a high-dimensional signal whose non-zero coefficients only arise in a few blocks from compressive measurements. However, most off-the-shelf data-driven reconstruction networks do not exploit the block-sparse structure. Thus, they suffer from deteriorating performance in block-sparse signal recovery. In this paper, we put forward a block-sparse reconstruction network named Ada-BlockLISTA based on the concept of deep unfolding. Our proposed network consists of a gradient descent step on every single block followed by a block-wise shrinkage step. We evaluate the performance of the proposed Ada-BlockLISTA network through simulations based on the signal model of two-dimensional (2D) harmonic retrieval problems.

1. INTRODUCTION

Compressive sensing (CS) plays an indispensable role in the field of signal processing [1]–[3]. The goal is to recover an unknown, sparse signal from noisy observations taken from a known, under-determined dictionary, with N < M. Noisy observation y G C^N can be formulated as

$$\begin{equation*}{\mathbf{y}} = {\mathbf{\Phi }}{{\mathbf{x}}^{\ast}} + {\mathbf{w}},\tag{1}\end{equation*}$$ where is the ground truth signal, and is additive random noise present in the system.