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

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.

[1]  Prateek Jain,et al.  One-Bit Compressed Sensing: Provable Support and Vector Recovery , 2013, ICML.

[2]  Ping Li,et al.  One Scan 1-Bit Compressed Sensing , 2015, AISTATS.

[3]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[4]  Richard G. Baraniuk,et al.  1-Bit compressive sensing , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[5]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[6]  Qian Chen,et al.  A Fast and Accurate Two-Stage Algorithm for 1-bit Compressive Sensing , 2013, IEICE Trans. Inf. Syst..

[7]  Deanna Needell,et al.  Two-Part Reconstruction With Noisy-Sudocodes , 2014, IEEE Transactions on Signal Processing.

[8]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[9]  Laurent Jacques,et al.  Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors , 2011, IEEE Transactions on Information Theory.

[10]  Yaniv Plan,et al.  One-bit compressed sensing with non-Gaussian measurements , 2012, ArXiv.

[11]  Jinfeng Yi,et al.  Efficient Algorithms for Robust One-bit Compressive Sensing , 2014, ICML.

[12]  Dacheng Tao,et al.  Hamming Compressed Sensing , 2011, ArXiv.

[13]  E. Candès.  The restricted isometry property and its implications for compressed sensing , 2008 .

[14]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[15]  Sun Biao,et al.  Investigation of sign spectrum sensing method , 2011 .

[16]  Robert D. Nowak,et al.  Sample complexity for 1-bit compressed sensing and sparse classification , 2010, 2010 IEEE International Symposium on Information Theory.

[17]  Yaniv Plan,et al.  One‐Bit Compressed Sensing by Linear Programming , 2011, ArXiv.

[18]  P. Boufounos.  Greedy sparse signal reconstruction from sign measurements , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[19]  Petros Boufounos,et al.  Reconstruction of sparse signals from distorted randomized measurements , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

[20]  Ming Yan,et al.  Robust 1-bit Compressive Sensing Using Adaptive Outlier Pursuit , 2012, IEEE Transactions on Signal Processing.

[21]  Wotao Yin,et al.  Trust, But Verify: Fast and Accurate Signal Recovery From 1-Bit Compressive Measurements , 2011, IEEE Transactions on Signal Processing.

[22]  Yaniv Plan,et al.  Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach , 2012, IEEE Transactions on Information Theory.