基于混沌和统计学习的动态压缩测量理论研究

Dynamic compressed sensing is a new theory developed on traditional compressed sensing, which is aiming at the compressed sampling and reconstruction of dynamic signal. Dynamic signal is always with slow time-varying sparsity patterns and certain temporal-correlation in adjacent time, which means its support, sparsity and the coefficient of non-zero elements change slowly over time. The essential of dynamic compressed sensing lies on three parts: the measured signal is dynamic evolved over time, the measurement matrix needs to satisfy the dynamic restricted isometry property (RIP), the reconstruction algorithms needs to take temporal-correlation of dynamic signal into account. In order to fully exert the dynamic characteristics of dynamic signal and improve the whole recovery performance of dynamic compressed measurement, this research program proposes the systematic theoretical research of dynamic compressed measurement based on chaos and statistical learning. .The research contents consist of the following five parts: (1) the construction of the chaotic dynamic compressed measurement matrices will be investigated based on dynamic RIP; (2) the signal reconstruction and the evaluation of the recovery performance will be exploited from the chaotic dynamic compressed measurements; (3) a novel signal recovery approach based on statistical learning will be designed suitable to the chaotic dynamic compressed measurements; (4) the signal reconstruction from the chaotic dynamic compressed measurements contaminated with noise will be specially considered and the reconstruction algorithm of combining chaos filtering with statistical learning will be proposed; (5) some typical applications of chaotic dynamic compressed measurement will be researched in a cross field of electrical and mechanical engineering..The above research contents will have great theoretical and practical significance for building the system framework of dynamic compressed measurement and promoting its engineering applications.

动态压缩感知是针对动态信号的压缩采样与重构而发展起来的一个新方向。动态信号的支撑集、稀疏度以及非零元素的系数一般随时间缓慢变化，相邻时刻的信号之间存在一定的关联性；动态压缩测量矩阵需要满足动态RIP条件；动态信号的重构需要充分利用动态信号的特性。为充分挖掘动态信号的特性、提升动态信号压缩测量的整体性能，本申请项目将统计学习和混沌引入动态压缩感知领域，提出对基于混沌和统计学习的动态压缩测量理论进行系统研究。主要包括：（1）基于动态RIP理论的混沌动态压缩测量矩阵的构造；（2）混沌动态压缩测量信号的重构与性能评估；（3）基于统计学习的混沌动态压缩测量信号的重构及性能评估；（4）混沌滤波与统计学习相结合的混沌动态压缩测量信号的重构与性能评估；（5）混沌动态压缩测量在典型实际问题中的应用。以上内容的研究，对构建全新的动态压缩测量理论体系框架、推动动态压缩感知的工程应用具有重要的理论和实际意义。

本项目旨在发展压缩感知理论，从静态压缩感知走向动态压缩感知，本项目聚焦基于混沌和统计学习相结合的动态稀疏信号压缩测量新理论和新方法研究，并尝试将新方法应用于工程实际。.本项目的主要研究内容包括：.（1）基于动态RIP理论的混沌动态压缩测量矩阵的构造；（2）混沌动态压缩测量信号的重构与性能评估；（3）基于统计学习的混沌动态压缩测量信号的重构及性能评估；（4）混沌滤波与统计学习相结合的混沌动态压缩测量信号的重构与性能评估；（5）混沌动态压缩测量在典型实际问题中的应用。.本项目的重要结果有以下8个方面：.1）提出了基于动态RIP理论的混沌动态压缩测量矩阵的构造方法。.2）提出了混沌动态压缩测量的信号重构与性能评估方法。.3）提出了基于统计学习的混沌动态压缩测量的信号重构及性能评估方法。.4）提出了基于卷积高斯混合模型（convolutional Gaussian mixture models）和贝叶斯理论的动态压缩测量信号的重构方法。.5）提出了基于稀疏贝叶斯学习残差重构的动态压缩感知信号重构算法（SBL-R-DCS）。.6）提出了分块稀疏贝叶斯学习残差重构的动态压缩感知信号重构算法（Block-SBL-R-DCS）。.7）提出了快速变化的视频序列动态压缩信号重构算法。.8）开展了实时视频动态信号的压缩测量应用研究和油气管道内检测器阵列信号的压缩测量应用研究。.基于本项目研究，培养博士研究生1人、硕士研究生1人。在国际国内重要刊物上公开发表了有份量的学术论文。.本项目的科学意义：.实际工程中存在众多的实时动态大数据，实时动态大数据的安全采样非常具有挑战性、实用性。本项目（51677094）连同上一个自然基金项目（51277100）的研究，解决了实时大数据动态信号的压缩采样、信号重构的科学问题，而且结合国家重大需求，将本项目的成果应用于高速高清油气管道内检测器。本项目的研究工作集科学性和实践性为一体。