A Robust Decoder for 1-bit Compressed Sensing

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:2021-07-23 15:00





In 1-bit compressive sensing (1-bit CS) where a target signal is coded into a binary measurement, one goal is to recover the signal from noisy and quantized samples. Due to the presence of nonlinearity, noise, and sign flips, it is quite challenging to decode from the 1-bit CS. In this talk, we consider a least squares decoder for several different setting: overdetermined system, with L1-penalty, with vardinality constraint, and with low generative intrinsic dimension. For each case, we show with high probability, the least squares solution approximates the signal up to a constant.  Numerical experiments are presented to illustrate the robustness of the proposed model.


吕锡亮,武汉大学教授,博士生导师,青年长江学者;本科毕业于北京大学,并于新加坡国立大学获得硕士、博士学位;20071月至6月,赴美国马里兰大学做访问学者,20078月至20107月,在奥地利科学院RICAM研究所从事博士后研究,2017年入选教育部长江学者奖励计划青年学者;主要研究方向包括稀疏重构的算法与应用、偏微分方程数值解、最优控制、以及反问题的理论和算法等;研究成果已发表在国际重要的应用数学和计算数学期刊上,包括 SIAM系列、NMMCACHAMPJMLRIP等。