结构化压缩感知及其在盲信号处理中的应用

项目名称： 结构化压缩感知及其在盲信号处理中的应用

项目编号： No.61503047

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 自动化技术、计算机技术

项目作者： 邹健

作者单位： 长江大学

项目金额： 20万元

中文摘要： 压缩感知是建立在数学理论基础上的一种全新的信息获取与处理的理论框架，是近年来信号处理、系统辨识和模式识别领域的研究热点之一．传统的压缩感知模型中没有充分利用信号的稀疏结构这个先验信息．事实上，利用信号的稀疏结构可以得到更好的重构效果．本项目将在前期针对分块稀疏这一特殊的稀疏结构进行研究的基础上，对结构化压缩感知展开研究，主要研究内容包括：针对不同的稀疏结构，构造统一、简洁的稀疏度量函数，并将将新的稀疏度量函数与压缩感知框架结合，建立统一的结构化压缩感知模型；针对该模型设计快速算法，新算法将考虑结构化压缩感知问题中目标函数非光滑等特性，只利用目标函数的一阶导数信息，具有较低的计算复杂度，适用于大规模问题的求解；将结构化稀疏模型用在盲信号处理中，去除信号采集中出现的脉冲噪声，以更好的分离源信号和辨识信道．本项目的研究使得结构化压缩感知在理论和应用上都具有良好的扩展性，具有一定的理论和应用价值.

中文关键词： 压缩感知；稀疏表示；盲辨识；收敛性

英文摘要： Compressive Sensing (CS) is an new developed theoretical framework for information acquisition and processing, which is based on mathematics theory. CS is one of the hottest research topic in signal processing, system identification and pattern recognition. However, the conventional CS model consider the sparsity without the additional structure information. In fact, structured sparsity will lead better reconstruct result. This project is focus on structured compressive sensing problem, which is based on the research of block-sparse representation. The main contributions of this project are as follows: Firstly, based on the internal relationship between the sparse elements, we will build an unified and brief frame to measure the different sparse structure. Further more, we will build a new structured compressive sensing model by combining the proposed sparse measurement with compressive sensing model. Secondly, we will propose fast algorithms for large-scale structured compressive sensing. The proposed algorithms deal with the non-smoothness of the objective function in structured CS problem, which has low iteration complexity and suitable for large-scale problem since it just only use the first order derivative of the objective function. Finally, we will give a blind source denoising method in the presence of impulsive noise by the structrued sparse model. The proposed project has a certain potential theoretical and application value since it expand the theory and application range of structured compressive sensing.

英文关键词： Compressive sensing;Sparse representation ;Blind identification;Convergence