基于系统参数化理论的信号稀疏表示和观测系统优化设计

Compressed sensing is a novel sampling framework which has broken through the traditional signal samping mode and provided a new method to alleviate the pressure of demand for the huge amounts of information. Therein, signal sparse representaion and incoherent measurement are the key to the success of the CS techniques. However so far the analysis model is lack of in-depth research and the dictionary is not adaptive the signal characteristics. In this project, aiming at these key problems, a new dictionary design concept is proposed and a novel incoherent measurement system is investigated. Firstly, the optimization model between the signal, system parameters and sparse coefficients is proposed with the help of the theories of signal modeling, system structures and optimization techniques. The signal-adapted dictionary is realized by the structure parameters of the optimal system. Secondly, an incoherent measurement system is designed for the given dictionary based on the tight frame theory and gradient algorithm. And the infulence of the dictionary and projection matrix on the signal reconstuction with high probability will be studied profundly. At last, as applications, the speech proccesing CS system is exploited for the speech reconstruction and denoising using the analysis model. The outcomes of this project will provide important theoretical guidance and a solid foundation for applications in the areas such as audio, image and wireless network.

压缩感知理论以一种新的采样框架突破了传统的数字信号采样方式，为缓解人们对巨量信息的需求压力提供了一种全新的方法。其中，信号稀疏表示和非相干观测直接影响着感知的效率，而目前研究成果对信号稀疏表示中的分析模型仍缺乏深入的理论探讨，尤其是信号字典无法做到与信号自适应。本项目旨在针对该关键问题提出一种新型信号字典设计方法并构建非相干观测系统，具体研究内容包括：1)基于信号建模、系统结构理论和优化算法，建立信号、系统参数和稀疏系数三者之间的优化模型，以最优系统结构参数设计信号字典，实现信号-字典间自适应；2)基于紧框架理论和梯度算法，构建字典优化下的非相干观测系统，明确字典和观测矩阵对高概率重构信号的影响机制；3)在此基础上，构建语音处理应用框架，实现稀疏表示分析模型在CS系统中的语音重构和消噪。本项目研究工作将为音频、图像、无线网络等应用领域提供重要理论依据和应用价值。

压缩感知(Compressed Sensing-CS)理论是基于信号的可压缩性，通过非相关观测来感知高维信号，并从低维观测数中高概率重构出原信号，它为解决人们对巨量信息的需求压力提供了一种有效的解决方法。其中信号的稀疏表示和观测采样是信号高精度重构的关键。本项目重点研究压缩感知系统中稀疏字典和观测矩阵优化设计算法，以及其在图像、语音等领域的应用，主要包括：(1) CS系统中的观测矩阵优化设计，基于紧框架理论，构造Gram矩阵与ETF阵的逼近模型，减小字典和观测矩阵的相干系数；并讨论了存在信号稀疏表示误差时的观测矩阵优化设计方法；(2)基于信号特征的自适应字典学习，根据信号的应用背景，改进了现有的冗余字典学习算法，提高了字典学习的速度；(3)字典和观测矩阵的联合优化，提出了一种新的联合优化模型，采用交替优化方法，得到了稀疏字典和观测矩阵的解析解，针对于图像信号，结果显示其重构精度要高于现有的优化算法；4）基于以上的理论研究，探讨了压缩感知理论在人脸识别、图像修复、图像去噪、语音等领域的应用，重点设计了与信号特性相匹配的信号字典，及与信号字典相干性小的观测矩阵。本项目的研究成果对CS理论在相关领域中的应用具有重要的理论指导意义。