Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices

  • A+

:丁维洋
:2021-07-22 15:20
:厦大海韵园实验楼105报告厅

报告人:丁维洋(复旦大学)

 间:2021722日下午15:20

 点:厦大海韵园实验楼105报告厅

内容摘要:

Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure quaternion matrix can be obtained by using the quaternion singular value decomposition. However, this approximation is not optimal in the sense that the resulting low-rank approximation matrix may not be pure quaternion, i.e., the low-rank matrix contains real component which is not useful for the representation of a color image. The main contribution of this talk is to find an optimal rank-r pure quaternion matrix approximation for a pure quaternion matrix. Our idea is to use a projection on a low-rank quaternion matrix manifold and a projection on a quaternion matrix with zero real component, and develop an alternating projections algorithm to find such optimal low-rank pure quaternion matrix approximation. The convergence of the projection algorithm can be established by showing that the low-rank quaternion matrix manifold and the zero real component quaternion matrix manifold has a non-trivial intersection point. Numerical examples on synthetic pure quaternion matrices and color images are presented to illustrate the projection algorithm can find optimal low-rank pure quaternion approximation for pure quaternion matrices.

个人简介:

丁维洋博士分别于2011年和2016年在复旦大学获学士和博士学位,随后在香港理工大学作博士后研究,20179月至202011月在香港浸会大学任研究助理教授,其后于202011月加入复旦大学类脑智能科学与技术研究院,担任青年研究员。丁博士的主要研究兴趣包括结构矩阵、张量计算和优化及其在脑与类脑科学、数据分析、信号处理等领域的应用。丁博士已出版学术专著1本,发表高质量期刊论文15篇(包括SIAM系列,JSCLAA等),其中有3篇是ESI高被引论文。目前,他主持国家自然科学基金委的青年科学基金项目以及一项上海求索杰出青年计划项目。


联系人:杜魁教授