一、题目：Blind Deconvolution and Nonconvex Regularization Algorithm
二、主讲人：浙江大学求是特聘教授，博士生导师李松
三、时间：11月30日(周五)下午2：30开始
四、地点：A4-305报告厅
摘要：In this talk, we consider the multichannel blind deconvolution problem. We wish to
estimate the input signal and blur kernels simultaneously. Existing theoretical results
showed that the original inputs are identifiable under subspace assumptions. However, the subspaces discussed before were randomly or generically chosen. Here, we
propose deterministic subspace assumption, which is widely used in practice, and give some theoretical results. We derive tight sufficient condition for identifiability of
signal and convolution kernels, which is only violated on a set of Lebesgue measure
zero. Then, we present a nonconvex regularization algorithm and show that the global minimizer of the proposed nonconvex algorithm is rank-one matrix under mild
conditions on parameters and noise level. The stability result is also shown under the assumption that the inputs lie in a compact set. Finally, we provide numerical
experiments to show that our nonconvex regularization model outperforms convex
relaxation models, such as nuclear norm minimization and some nonconvex methods, such as alternating minimization method and spectral method.
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）。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。
欢迎广大师生参！（联系人：李亚玲）
理学院
应用数学研究所
