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 one-bit 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.

Keywords

• compressive sensing
• complex
• binary
• bipolar
• sigmoid
• reconstruction
• sparse signal processing