Exploiting Two-Dimensional Group Sparsity in 1-Bit Compressive Sensing

Abstract

We propose a new approach, two-dimensional fused binary compressive sensing (2DFBCS) to recover 2D sparse piece-wise signals from 1-bit measurements, exploiting 2D group sparsity for 1-bit compressive sensing recovery. The proposed method is a modified 2D version of the previous binary iterative hard thresholding (2DBIHT) algorithm, where the objective function includes a 2D one-sided _1 (or _2) penalty function encouraging agreement with the observed data, an indicator function of K-sparsity, and a total variation (TV) or modified TV (MTV) constraint. The subgradient of the 2D one-sided _1 (or _2) penalty and the projection onto the K-sparsity and TV or MTV constraint can be computed efficiently, allowing the appliaction of algorithms of the forward-backward splitting (a.k.a. iterative shrinkage-thresholding) family. Experiments on the recovery of 2D sparse piece-wise smooth signals show that the proposed approach is able to take advantage of the piece-wise smoothness of the original signal, achieving more accurate recovery than 2DBIHT. More specifically, 2DFBCS with the MTV and the _2 penalty performs best amongst the algorithms tested.

Tasks

Reproductions