A Compressed Sensing Recovery Algorithm Based on Support Set Selection

Abstract

The theory of compressed sensing (CS) has shown tremendous potential in many fields, especially in the signal processing area, due to its utility in recovering unknown signals with far lower sampling rates than the Nyquist frequency. In this paper, we present a novel, optimized recovery algorithm named supp-BPDN. The proposed algorithm executes a step of selecting and recording the support set of original signals before using the traditional recovery algorithm mostly used in signal processing called basis pursuit denoising (BPDN). We proved mathematically that even in a noise-affected CS system, the probability of selecting the support set of signals still approaches 1, which means supp-BPDN can maintain good performance in systems in which noise exists. Recovery results are demonstrated to verify the effectiveness and superiority of supp-BPDN. Besides, we set up a photonic-enabled CS system realizing the reconstruction of a two-tone signal with a peak frequency of 350 MHz through a 200 MHz analog-to-digital converter (ADC) and a signal with a peak frequency of 1 GHz by a 500 MHz ADC. Similarly, supp-BPDN showed better reconstruction results than BPDN.