报告题目：One-Bit Compressive Sensing with Projected Subgradient Method under Sparsity Constraints

报告人：李松教授（浙江大学）

报告时间：2018年12月21 日下午2：00-3：00      

报告地点：老主楼321      

摘要：One-bit compressive sensing theory shows that sparse signals can be almost exactly reconstructed from a small number of one-bit quantized linear measurements. This talk presents the convergence analysis of the binary iterative hard thresholding (BIHT) algorithm which is a state-of-the-art recovery algorithm in one-bit compressive sensing. The basic idea of the convergence analysis is to view BIHT as a kind of projected subgradient method under sparsity constrains. To the best of our knowledge, this is the first convergence analysis of BIHT. We consider a general convex function subject to sparsity constraints and connect it with the non-convex model in one-bit compressive sensing literatures. A projected subgradient method is proposed to solve the general model and some convergence results are established. Furthermore, the corresponding stochastic projected subgradient method is provided with convergence guarantee. Then we also apply the projected subgradient method to some related non-convex optimization models arising in compressive sensing with `1-constraint, sparse support vector machines and rectifier linear units regression. Finally, some numerical examples are presented to show the validity of our convergence analysis.          

报告人简介：李松，浙江大学求是特聘教授，博士生导师，研究方向包括；压缩感知理论、低秩矩阵恢复理论、相位恢复理论以及双线性反问题（如：盲卷积重构问题等）。代表性工作曾获得教育部自然科学二等奖（排名1）。此外，主持了国家自然科学基金重点项目与面上项目等5项基金项目，也主持了浙江省重大科技专项的基金项目。到目前为止在国际主流期刊发表了80余篇学术论文，其中包括：《Appl.Comput.Harm. Anal》、《J.Fourier.Anal.Appl》、《IEEE.Trans.Signal.Processing》、《J.Approx.Theory》、《Inverse Problem and Imaging》、《IEEE Trans.Inform.Theory》等国际数学重要期刊以及国际数学与信息以及信号处理交叉领域顶级期刊。他曾被邀请参加数十次国际重要学术会议，并做特邀报告，其中包括《亚洲逼近论会议》一小时特邀报告以及《第七届世界华人数学家大会》45分钟特邀报告等。他曾担任国家自然科学基金委重点项目与面上项目评审会评专家。

邀请人：陈迪荣