Towards a Lower Sample Complexity for Robust One-bit Compressed Sensing

Abstract

In this paper, we propose a novel algorithm based on nonconvex sparsity-inducing penalty for one-bit compressed sensing. We prove that our algorithm has a sample complexity of O(s// 2) for strong signals, and O(s log d// 2) for weak signals , where s is the number of nonzero entries in the signal vector, d is the signal dimension and is the recovery error. For general signals, the sample complexity of our algorithm lies between O(s// 2) and O(s log d// 2). This is a remarkable improvement over the existing best sample complexity O(s log d// 2). Furthermore, we show that our algorithm achieves exact support recovery with high probability for strong signals. Our theory is verified by extensive numerical experiments , which clearly illustrate the superiority of our algorithm for both approximate signal and support recovery in the noisy setting.

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