基于混沌的压缩测量理论及其应用

Conventional signal sampling is experiencing a tremendous change called compressive sampling that goes against the common knowledge. Compressive measurement is an extension of compressive sampling in engineering areas in which the measurement matrix is a crucial technology such as designing and the circuit's implements as well as the performances under the noisy environments...Most measurement matrices developed so far are based on randomization and the obvious disadvantages exist. The circuits implement is not feasible to the generation of matrix element and the compressed inner product. The test to the Restricted Isometry Property of the matrices is absent of operation in practice. Both the compressed measurements and the inevitable noise are random in essence so that the discrimination is difficult. ..In this proposal, the chaotic sequences are utilized to the compressive measurement matrices and advantages will be benefit from it. The randomness of chaos will satisfy the incoherence of the matrices and the deterministic character of chaos is suitable to the circuit implements. The most distinguished character is that the chaotic compressed measurements and the noise are entirely different in the phase space in which the discriminating and denoising could be performed...The research program is consisting of the following six parts. Firstly, the construction approaches of the chaotic measurement matrices will be investigated based on the probabilistic and isotropic theory. Secondly, the signal reconstruction and the evaluation of the recovery performance will be exploited from the chaotic compressed measurements, as well as the comparison to the conventional algorithms. Thirdly, a novel signal recovery approach based on chaotic theory will be designed suitable to the chaotic compressed measurements. Fourthly, the signal reconstruction from the chaotic compressed measurements contaminated with noise will be specially considered and the performance of the recovery will be evaluated. Fifthly, the circuit's implements approach will be researched for the chaotic compressive measurements. Finally, some typical applications will be designed and demonstrated of the chaotic compressive measurement in a cross field of electrical and mechanical engineering. ..A new theoretical paradigm of chaotic compressive measurements will be constructed and the deterministic compressive measurement will be extended, and the solid basis will be provided and practical engineering applications will be also demonstrated through aforementioned research works.

传统的信号采样正在经历一场压缩采样的伟大变革。压缩测量是压缩采样的工程化拓展，压缩测量矩阵的设计与电路实现以及在噪声环境下的性能是其关键所在。已有的随机型压缩测量矩阵在实际应用中存在着明显的缺陷：矩阵元素的生成和压缩运算无法用硬件电路实现；矩阵的有限等距特性的检验缺少可操作性；压缩测量与噪声都为随机性、难以区分。本项目将混沌序列用于压缩测量矩阵，其优越性在于：混沌的随机性满足非相干性；混沌的确定性适合于电路实现；压缩测量的混沌性有利于区分和减弱噪声。研究内容包括：基于概率和迷向理论的混沌测量矩阵的构造；混沌压缩测量中的信号重建与性能评估；基于混沌理论的信号重建与性能评估；噪声环境下混沌压缩测量中的信号重建与性能评估；混沌压缩测量的电路实现方法；混沌压缩测量在典型实际问题中的应用。本项目的研究将系统构建混沌压缩测量理论体系框架，丰富拓展压缩测量理论，为压缩测量的工程应用奠定基础、开拓新路。

本项目拟对混沌压缩测量理论和应用进行系统深入的研究，系统构建全新的混沌压缩测量理论体系框架。力争在混沌压缩测量矩阵的构建、利用混沌本质特征的信号重建方法、具有抗噪声性能的信号重建方案等方面做出独立新颖的学术贡献，并探索混沌压缩测量在典型实际问题中的应用。. 本项目在基于RIPLESS理论的混沌压缩矩阵构造理论、混沌循环测量矩阵最优构造理论、二进制信号混沌压缩测量信号重构理论方法，噪声对混沌压缩测量的影响、混沌压缩测量电路实现方法、混沌及其压缩测量在工程中的实际应用等方面开展了深入系统的研究工作。初步建立了混沌压缩测量的理论框架，发明了实时多通道大数据压缩采样新技术并将其应用于油气管道内检测器中，将油气管道内检测器的检测速度提高了近一倍，具有重大实际应用价值。