HISTORY: An Efficient and Robust Algorithm for Noisy 1-Bit Compressed Sensing

Biao SUN  Hui FENG  Xinxin XU  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E99-D   No.10   pp.2566-2573
Publication Date: 2016/10/01
Publicized: 2016/07/06
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2015EDP7438
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
Keyword: 
1-bit compressed sensing,  sign flips,  Hamming distance,  

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Summary: 
We consider the problem of sparse signal recovery from 1-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These sign flips may result in severe performance degradation. In this study, a novel algorithm, termed HISTORY, is proposed. It consists of Hamming support detection and coefficients recovery. The HISTORY algorithm has high recovery accuracy and is robust to strong measurement noise. Numerical results are provided to demonstrate the effectiveness and superiority of the proposed algorithm.