Phase Retrieval with Fourier Measurements
- A+
：Prof. Li Song
：2020-11-06 15:00
：Tencent Meeting APP
Speaker：Prof. Li Song
Zhejiang University
Title: Phase Retrieval with Fourier Measurements
Time：6th, Nov., 2020, 15:00
Location： 腾讯会议APP(线上)
Meeting Info： https://meeting.tencent.com/s/M6hqKusojoEN
会议 ID：722 980 579
会议密码：1106
Abstract:
In my talk, I shall consider the problem of phase retrieval from Fourier measurements. E. Candés, X. Li and M. Soltanolkotabi have researched this problem with random diffraction patterns. By using the Phase Lift approach, they originally proved that O(log4 n) coded different patterns suffice for perfect recovery of complex-valued signals. Moreover, they expected to reduce this measurement number as pointed out in their paper. Subsequently, D. Gross, F. Krahmer and R. Kueng provided different coded diffraction patterns with real masks. Then they demonstrated that the phase information can be exactly recovered from O(log2 n) coded diffraction patterns for complex-valued signals of odd dimensions. By establishing a modified key lemma, combined with PhaseLift method and the works of D. Gross, F. Krahmer and R. Kueng, we prove that O(log2 n) coded diffraction patterns are sufficient to recover real-valued signals of even dimensions. Furthermore, two kinds of Riemannian optimization algorithms, namely, Riemannian gradient descent algorithm (RGrad) and Riemannian conjugate gradient descent algorithm (RCG), are presented to solve such problem. The measurements number are only O(n log n) which is optimal.
Speaker Introduction：
李松，浙江大学求是特聘教授，博士生导师。主要研究领域包括；压缩感知理论及其应用、低秩矩阵恢复理论、相位恢复理论、盲去卷积理论以及小波框架理论等。主持了国家自然科学基金重点项目、面上项目、浙江省重大科技项目等项目，作为第一完成人曾获得教育部自然科学二等奖（2013）。分别在《Applied and Computational Harmonic Analysis》、《Journal of Approximation Theory》、《Journal of Fourier Analysis and Its Application》、《Advance in Computational Mathematics》、《IEEE Transcations on Information Theory》、《IEEE Transcations on Signal Processing》等国内外著名期刊发表90余篇学术论文。曾受邀多次参加重要国际学术会议，并做邀请报告，其中包括：世界华人数学家大会45分钟邀请报告(2016),亚洲逼近论会议1小时特邀报告（2003）等。
联系人：伍火熊
