Complex Phase Retrieval with Outliers

主讲人：李朋

摘要：Consider the task of recovering a vector x from phaseless linear measurements b that contain noise e and a constant fraction of gross arbitrary errors y. This nonconvex problem is called complex phase retrieval with outliers. Especially, when the unknown vector x is sparse, it is called complex sparse phase retrieval with outlier. In this paper, we show that we can find an solution x* from the observation b. We show that for  a small and any fraction of gross errors y, we can obtain an stable recovery error estimation with high probability. Furthermore, we also obtain an lower bound of the estimate error and prove that the obtained upper bound of recovery errors estimation are rate optimal. We also design an algorithm based on the proximal subgradient splitting method to solve this problem. The numerical tests show our method has good performance.

主讲人简介：李朋，兰州大学数学与统计学院副教授，当前研究兴趣为数据科学和机器学习, 包括压缩感知、低秩矩阵恢复、相位恢复、数学图像处理、数据聚类、稀疏优化算法等。他当前主持甘肃省自然科学基金项目、国家自然科学青年基金项目、中央高校基本业务费项目各一项。他取得了一系列研究成果,在Inverse Problems, Signal Process., Comput. Math.Appl. , J. Comput. Appl. Math.,  J. Math. Anal. Appl., Acta Mathematica Sinica等著名杂志发表学术成果近二十篇。

邀请人：刘海霞

时间：2022年10月2日（星期日）15:00-16:30