结构性稀疏信号的动态系统建模与恢复

Structured sparse model for signals describes both sparsity and structured property over the elements of the sparse signal vectors. Consequently, it can represent the signal characteristics more accurately and obtain better performance than sparse model.The state-of-the-art recovery algorithms based on structured sparse model are mostly discrete, iterative, and thus with large complexity and memory requirement. Consequently, they cannot be conveniently applied to real-time reconstruction. In this project, a dynamic model for structured sparse signals will be constructed via dynamic systems, and then a continuous dynamic reconstruction method will be proposed based on the system state observer theory. The importance of this project can be considered in two aspects: theoretically, the constructed dynamic model for structured sparse signals can be expected to provide a possible approach to nonlinear compressed sensing; practically, the proposed dynamic reconstruction method can be easily implemented by analog circuits, which might be exploited to real-time reconstruction for structured sparse signals in real applications.

结构性稀疏信号模型同时描述了信号的稀疏性及其稀疏变换矢量的结构性，能更加准确的描述信号的特征，因此往往能得到更好的处理结果。基于该信号模型，现有的结构性稀疏信号恢复算法大多是离散的迭代求解算法，需要较大的运算量和存储空间，因此不便于实时处理。本项目将首先构建结构性稀疏信号的动态模型，然后基于动态系统观测器原理，提出一种结构性稀疏信号的连续动态求解方法。其理论意义在于，本项目将构建一个结构性稀疏信号的动态模型，有望为非线性压缩感知理论提供一种新的思路。其实际意义在于，本项目提出的动态求解算法可以较容易的采用模拟电路实现，可以提供一种易于工程实现、且实时的结构性稀疏信号求解方法。

信号的稀疏性是信号处理中的一个非常重要的研究领域，稀疏信号的重建问题则是应用信号稀疏特性一个关键问题。同样的，结构稀疏性是也是稀疏信号处理中的重要研究方向之一；而研究如何高效率、高精度的结构稀疏重建算法则是应用结构稀疏性的一个关键步骤。本项目主要关注于结构性稀疏信号的重建问题，分别从统计的角度和模拟重建的角度出发，提出了基于局部Beta过程的结构性稀疏重建算法、自适应结构稀疏重建算法、以及基于连续动态系统的稀疏重建算法。基于项目的研究成果，项目组研究人员在国内外期刊和国际会议共发表学术论文11篇，包括1篇信号处理顶级期刊论文，5篇SCI检索期刊论文，1篇核心期刊论文，4篇EI国际会议论文。

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