鲁棒性压缩感知关键技术的研究

Compressed sensing is an emerging sampling technique and will have broad application prospects in many areas. In actual applications, noises may inevitably exist, and thus to study the robust compressed sensing technology is of great significance. This project intends to study the construction of robust sparse basis and projection operator, and design more robust recovery algorithms based on the features of noises so as to establish a robust compressed sensing system, improving the reconstruction performance and enhancing the utility of compressed sensing system. Our research includes: (1) Design of the iterative optimization algorithm of sensing matrices and the selection algorithm of optimal length of the measurement vector to improve the approximate orthogonality of projection operators and further enhance robustness; (2) Design of adaptive sensing matrices according to characteristics of speech signals to enhance the robustness of the projection operator in the compressed speech sensing system; (3) Construction of sparse bases or redundant dictionaries to enhance the robustness of speech signals in the transform domain; (4) Design of a pre-filtering system to achieve pre-processing of the measurement vector to enhance the robustness of the reconstruction system; (5) Design of more robust non-linear reconstruction algorithms; (6) Design of cooperative reconstruction algorithm for denoising based on distributed compressed sensing

压缩感知技术是一种新兴的采样技术，由于具有对未知信号边感知边压缩的特性，所以该技术在许多领域都有广阔的应用前景。在实际的应用中，噪声难以避免，因而研究具有鲁棒性的压缩感知系统具有重要意义。本课题拟研究构造具有鲁棒性的稀疏基和投影算子，根据噪声特性设计更具鲁棒性的重构算法，以建立具有鲁棒性的压缩感知系统，改善重构信号质量，增强系统实用性。研究内容包括：（1）设计观测矩阵迭代优化算法以及含噪环境下最优观测序列长度选取算法，以增强观测矩阵的近似正交性，增强其鲁棒性；（2）根据语音信号的特性设计自适应观测矩阵，以增强在语音信号压缩感知系统中投影算子的鲁棒性；（3）构造适合语音信号的稀疏基或冗余字典，以增强语音信号在变换域的鲁棒性；（4）设计重构系统前置滤波系统，对观测序列进行预处理，增强重构系统的鲁棒性；（5）设计更具鲁棒性的非线性重构算法；（6）设计基于分布式压缩感知的协作降噪重构算法

压缩感知(Compressed Sensing, CS)技术是一种新兴的压缩采样技术，由于其具有对未知信号边采样边压缩的特性，所以该技术在许多领域具有广阔的应用前景。该技术中的核心问题是信号的稀疏性表示/近似问题、压缩采样(投影)问题和重构问题，而通过求解非线性优化问题从少量非自适应、线性的观测中重构出稀疏信号的CS重构问题又起着举足轻重的作用；如何构造稳定、对观测数据要求少(反映了压缩比高)、计算复杂度低、收敛速度快的重构算法，一直是CS理论重构技术研究的主要内容和追求的目标。此外，在实际的应用中，噪声难以避免，所以研究压缩感知重构技术的鲁棒性，以改善重构信号质量，是十分重要和很有意义的课题。.本课题研究了实际环境中面临各种噪声条件时的压缩感知系统，同时研究了分布式压缩感知技术，课题将分布式压缩感知有效地应用到含噪信号的重构中。研究内容主要包括：.（1）鲁棒性抗噪投影算子的构建.（2）白噪声环境下信号鲁棒性的重构算法.（3）基于压缩感知和稀疏表示的鲁棒说话人识别技术.（4）鲁棒性分布式压缩感知及频谱感知技术.（5）脉冲噪声环境下绝对稀疏信号的鲁棒性压缩感知技术.（6）鲁棒性语音压缩感知的快速重构技术