One-Bit Compressed Sensing Using Smooth Measure of l0 Norm

Quantization of signals and parameters happens in all digital data acquisition devices. It is commonly regarded as a non-ideality of the system, and shall be taken into account when designing or analyzing a system. The topic of one-bit compressed sensing studies the effect of quantization in the extreme case where the samples are quantized with only one bit, i.e., the sign bit. The recovery of a sparse signal based on one-bit measurements is widely accomplished via thresholding methods or variants of l(1)-minimization techniques. In this paper, we introduce a recovery method arising from smoothing directly the l(0) pseudo-norm. While we numerically verify the superior performance of the proposed method compared to the state-of-the-art techniques in our simulations, we briefly discuss the convergence analysis of this method.