报告题目：Identifiability and Nonconvex Algorithm of Multichannel Blind Deconvolution

主 讲 人：李松

单 位：浙江大学

时 间：5月10日14:30

腾 讯 ID：896 580 066

摘 要：

In this paper, we consider the multichannel blind deconvolution problem, where we observe the output of channels h_i ∈ R^n(i = 1, ...,N) that all convolve with the same unknown input signal x ∈ Rn.We wish to estimate the input signal and blur kernels simultaneously. First of all, 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 by a lifting method and approximate the rank one constraint via the difference of nuclear norm and Frobenius norm. 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. Besides, the computation of our regularization model is carried out and any limit point of iterations converges to a stationary point of our model. 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.

简 介：

李松，浙江大学求是特聘教授，博士生导师，主要从事：小波分析理论、压缩感知、低秩矩阵恢复、相位恢复、盲去卷积等领域的研究工作。到目前为止，在国际重要期刊Appl.Comput.Harmon.Appl，IEEE.Trans.Inform.Theory，IEEE.Trans.Signal.Process，J.Four.Anal. Appl，J.Approx.Theory等发表了90余篇学术论文；作为第一完成人获得教育部自然科学奖二等奖（2013）；作为项目负责人，完成了国家自然科学基金重点以及面上项目6项，完成了浙江省重大科技专项等基金项目。特别值得指出的是，他在人才培养方面取得了突出成绩，已经毕业的研究生中1人获得国家自然科学优秀青年基金，1人入选教育部青年奖励计划，作为合作导师指导的博士后获得国家自然科学优秀青年基金。