稀疏信号驱动的时间序列信号盲分离优化模型及算法研究

Time series signal is a digital sequence in chronological order. Recently, researches on blind source separation (BSS) with temporally series signals based on sparse representation has become a research focus in signal processing field. However, there are many shortcomings about most of existing methods, such as, only focusing on the sparsity of source signals, and not fully considering the structure information of source signals. In this project, based on the generation model of signal, we will take the sparsity of innovation, i.e., drive signal as the assumption and incorporate the prior structural information into the design of the sparse model and algorithm, which make us study the BSS problem of time series signals from a new perspective and can improve the performance of the algorithm. Specifically, we will firstly establish the objective function, which includes the sparsity measure of drive signal and the statistical character of source signal. And then, some constraints, for example, the linear constraint and the constraint of the structure information should be considered during the building of the optimization model. After that, we will develop the sparse optimal algorithms with low complexity and good convergence in order to improve the algorithm's validity and practicability. This research not only provides reliable methodology for signal processing problem, but also promotes the cross-study of optimal theory and signal processing, which is of great scientific and practical importance.

时间序列信号是按时间顺序组成的一组数字序列，利用稀疏表示方法盲分离时间序列信号是当前信号处理领域的研究热点之一。但现有的研究大多基于时序信号自身的稀疏性假设，而且大多未充分考虑时序信号的内部先验结构特征信息。本项目将从时序信号的生成模型入手，以驱动信号的稀疏性为全新的研究切入点，将时序信号的先验结构特征融入稀疏优化模型的构建以及算法的设计过程，从全新的角度研究时序信号的盲分离问题，提高算法的性能。具体研究内容为：首先建立以驱动信号稀疏性和源信号间的统计特性度量为目标函数，结构特性约束和线性约束相结合的优化模型，并进一步发展低复杂度、收敛性好的稀疏优化算法，以增强算法的实用性。本项目的研究不仅为实际信号处理提供可靠的方法论，而且可以推动最优化理论与信号处理学科的交叉研究，具有较为重要的科学意义和实用价值。

近年来，稀疏信号恢复问题已经成为信号处理领域中一个非常引人关注的研究课题。许多研究者从不同的角度进行了相关研究，提出了众多有效地稀疏信号恢复算法，其中包括结构化稀疏信号表示算法。该类算法将信号的结构化先验信息融入到算法设计中，充分挖掘了稀疏信号的内部结构特性，大大提高了稀疏恢复算法的分离精度，目前已经成为信号处理领域中一个全新的研究方向。本项目将对结构化稀疏信号恢复问题进行研究，利用诸如稀疏分析模型等，分析信号的内部的结构特性，给出度量这些结构特性的指标，并提出相应的优化模型，构造适当的优化算法，从而提高信号的分离精度。具体来说，项目的主要研究内容包括：（一）针对心电信号的周期结构特性，提出了一个两阶段的稀疏生体信号恢复算法；（二）基于分析稀疏模型的信号恢复问题，构造了一系列非凸的稀疏推导函数作为目标函数并给出了有约束优化模型，并提出了双层优化算法用于解决此模型。（三）在稀疏低秩矩阵分解理论的框架下提出了三种方法处理单通道歌声与伴奏的分离问题。（四）针对复杂网络中捕获问题，研究了有向加权网络、具有无标度小世界性质的Apollonian网络、无标度分形网络、Koch分形网络以及一类经典分层式网络(1,3)-flower随机游走问题。