广义低秩矩阵重构算法及其应用研究

项目名称： 广义低秩矩阵重构算法及其应用研究

项目编号： No.61502024

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 计算机科学学科

项目作者： 王恒友

作者单位： 北京建筑大学

项目金额： 20万元

中文摘要： 低秩矩阵重构作为压缩感知理论在矩阵情形下的推广，已经成为一种新的高维信息处理工具，是目前研究的热点之一。然而，传统的低秩矩阵重构模型主要处理单个矩阵的低秩近似问题，在实际应用中往往需要将问题进行转换，并构造出单个近似低秩的矩阵，这给该理论的应用带来不便。广义低秩矩阵恢复模型对其进行改进，实现了多矩阵的直接低秩近似，但已有的模型对稀疏大噪声等鲁棒性不好。为此，本项目拟以多矩阵的批量低秩近似为目标，综合开展广义低秩矩阵重构理论及应用研究，主要内容包括：(1)构建鲁棒广义低秩矩阵恢复模型，设计性能稳定的恢复算法；(2)建立广义低秩矩阵填充模型，给出性能良好的填充算法；(3)探索基于广义低秩矩阵重构的相似图像集或视频序列恢复方法。通过本项目的完成，不仅为低秩矩阵重构理论的发展提供新的思路，而且有助于进一步推动该理论在图像处理中的实际应用。

中文关键词： 广义低秩矩阵重构；低秩矩阵恢复；矩阵填充；图像恢复；稀疏大噪声

英文摘要： Low-rank matrix reconstruction as the generalization of compressed sensing theory in the case of a matrix has become a new kind of high-dimensional information processing tool. It is one hot issue of present study. However, the conventional low-rank matrix reconstruction theory is mainly process the problem of single matrix’s low-rank approximation. It often needs to convert the problem and construct an approximate low-rank matrix in practical applications, which is inconvenient to the application of the theory. The generalized low-rank approximations of matrices as the improved model have achieved the low-rank approximation for a collection of matrices, but it is not robust for sparse big noise. Thus, this project is intended to carry out a comprehensive study of the theory and application of generalized low-rank reconstructions of matrices. It mainly concludes as follows. Firstly, construct the model of robust generalized low-rank recoveries of matrices and design a stable algorithm. Secondly, construct the model of robust generalized low-rank completions of matrices and design a good performance algorithm. Finally, research recovering method of similar set of images or video sequences based on the model of generalized low-rank reconstructions of matrices. It not only provides new idea for development of low-rank reconstructions of matrices theory, but also promotes its practical application in image processing by the completion of this project.

英文关键词： generalized low-rank reconstructions of matrices ;low-rank matrix recovery ;matrix completion;image recovery;large sparse noise