基于压缩感知,矩阵填充和鲁棒的主成分分析的四元数信号处理方法研究

项目名称： 基于压缩感知,矩阵填充和鲁棒的主成分分析的四元数信号处理方法研究

项目编号： No.61201344

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 伍家松

作者单位： 东南大学

项目金额： 26万元

中文摘要： 压缩感知，矩阵填充和鲁棒的主成分分析是近年来新提出的数据获取理论，目前已经被广泛应用于信号与图像处理领域。四元数理论因其适合于彩色图像处理近年来也吸引了众多学者的关注。本项目旨在将压缩感知和矩阵填充理论与四元数理论结合，并将其应用于四元数域信号与图像处理，着重解决以下三个方面的问题：(1)解决四元数压缩感知恢复算法涉及的两类优化问题，将其应用到四元数彩色图像稀疏恢复和欠定系统四元数信号盲源分离；(2)解决四元数矩阵填充恢复算法涉及的两类优化问题，将其用于四元数傅里叶变换相位恢复；(3)解决四元数鲁棒的主成分分析恢复算法涉及的两类优化问题，提出四元数鲁棒的主成分分析的彩色图像处理方法。

中文关键词： 压缩感知；矩阵填充；鲁棒的主成分分析；四元数；信号与图像处理

英文摘要： Compressed sensing (CS), matrix completion (MC) and robust principal component analysis (RPCA) are the new data acquisition theories proposed in recent years. They have been widely used in signal and image processing fields. Quaternion algebra theory has also attracted the attention of many researchers recently because it is very suitable for color image processing. The project aims to combine the theory of CS and MC with that of quaternion algebra and also apply them to quaternion domain signal and image processing. We will place emphasis on the following three problems: (1) solve two types of optimization problems that involved in quaternion CS recovery algorithm and apply them to quaternion color image sparse recovery and underdetermined quaternion signal blind source separation; (2) solve two types of optimization problems that involved in quaternion MC recovery algorithm and apply them to quaternion Fourier transform phase retrieval; (3) solve two types of optimization problems that involved in quaternion RPCA recovery algorithm and propose the method of quaternion color image processing based on quaternion RPCA.

英文关键词： compressed sensing；matrix completion；robust principal component analysis；quaternions；signal and image processing