Analysis of noise in complex-valued binary and bipolar sigmoid compressive sensing

Abstract

Binary compressive sensing (CS) is a relatively new idea in the theory of sparse signal reconstruction. Under this framework, the signal is reconstructed based on the sign of the available measurements. This paper analyzes basic onebit CS concepts for the case of complex valued random Gaussian measurement matrices. The reconstruction is compared with the B-bit quantized measurements. The concept of binary CS-based reconstruction is generalized by applying a sigmoid function to the measurements. Noise influence is also considered. The reconstruction is performed using a simple iterative thresholding algorithm.