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

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。

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.