Collaborative Research: Dynamic Blind Source Separation

盲源分离（BSS）是指从线性混合信号中识别出源信号，传统的盲源分离方法仅限于静态混合信号。此外，这种方法通常依赖于难以利用和不健全的假设源统计。相比之下，所提出的研究解决了分离动态混合信号的一般问题，同时识别动态以及输入源。在制定相关的不适定系统识别问题的基本工具是稀疏性的概念，这是用来作为一个正则化项，以限制在一个自然的方式输入/过程动态的选择。拟议的研究将受益于一个相当强大的理论计算易处理的稀疏诱导优化，基于ℓ 1-泛函，这已经在最近几年形成。拟议的计划开始与一般的动态混合物模型的分析，exploringsparsity作为一个正则化项。这种模型的动机源于系统识别，分布式传感，以及在频谱分析，子空间识别和天线阵列的问题。该建议继续与专门的形式主义意图捕捉，在一个类似的框架，延迟/相干性分析以及系统识别的问题，在一个非平稳/非线性混合设置的大纲。为此，有人建议，联合稀疏的概念？相关分量分析的一种形式，是用于识别源、谐波等之间的共性的合适工具，同时寻找存在时间延迟和非线性混合的指示信号。该建议涵盖了一些详细的情况下，自回归动态导致凸优化问题。噪声，模型阶数和稳定性之间的权衡提出并纳入拟议的研究计划。BSS和图像分割技术之间的联系？一种形式的几何BSS，突出的方式，建议另一个概念的角度，拟议的研究。最后，讨论了词典设计的问题，即，如何获得合适的？过度完整？源信号和可能的系统动力学的基础上，根据先验信息和现有数据，在某种程度上，将确保一定程度的鲁棒性和可计算性，同时促进sparsity.Intellectual优点：实际以及理论问题将调查方面，而无处不在的系统动力学和信号传输路径的识别问题，在未知的干扰和输入的存在。的形式主义是投在盲源分离的背景下，和基本的新工具是稀疏性的概念，相对于适当选择的信号集合作为建模的选择规则。该方法受益于近年来取得成果的稀疏表示/压缩感知理论。从一个新的角度出发，提出了时延估计、相干性分析、非线性和非平稳建模等问题。在测量的时间序列的联合稀疏表示中寻找相关信息。一个潜在的变革性的广泛的工具可能会导致从新的分析和系统识别的方式在此提出。更广泛的影响：研究可能会影响非常不同的领域，如物理？在校准和过滤测量，图像分析？在MRI/医疗成像，系统识别，声学和抖动控制，通信？噪声和共振通道中的盲解卷积，雷达处理等。

Blind source separation (BSS) refers to the task of identifying sources from their linear mixtures.Traditional approaches to BSS have been limited to static mixtures. Furthermore, such approaches typically rely upon hard-to-exploit and non-robust assumptions on source-statistics. In contrast, the proposed research addresses the general problem of separating dynamically-mixed signals by simultaneously identifying both the dynamics as well as the input sources. The basic tool in the formulation of relevant ill-posed system identification problems is the notion of sparsity which is used as a regularization term to limit the choices of input/process dynamics in a natural way. The proposed research stands to benefit from a rather powerful theory on computationally-tractable sparsity-inducing optimization, based on ℓ1-functionals, which has taken shape in recent years.The proposed plan begins with an analysis of a general dynamic-mixtures-model, exploringsparsity as a regularizing term. Motivation for such models stems from system identification, distributed sensing, as well as problems in spectral analysis, subspace identification, and antenna arrays. The proposal continues on with an outline of specialized formalisms intent on capturing, in a similar framework, problems of delay/coherence analysis as well as of system identification in a non-stationary/nonlinear-mixing setting. To this end, it is proposed that the notion of joint sparsity?a form of dependent-component-analysis, is a suitable tool for identifying commonalities between sources, harmonics, etc., while seeking tell-tale signs of the presence of time-delays and of nonlinear mixing. The proposal covers in some detail the case of autoregressive dynamics which leads to a convex optimization problem. Tradeoffs between noise, model order, and stability are raised and integrated into the proposed research plans. Connections between BSS and image segmentation techniques?a form of geometric BSS, are highlighted in a way which suggests another conceptual angle for the proposed research. Finally, the issue of dictionary design is being discussed, i.e., how to obtain a suitable ?over-complete? basis for source signals and possibly system dynamics as well, based on prior information and on available data, in a way that will ensure a degree of robustness and computability while promoting sparsity.Intellectual Merit: Practical as well as theoretical questions will be investigated with regard to the rather ubiquitous identification problem for system dynamics and signal transmission paths, in the presence of unknown disturbances and inputs. The formalism is cast in the context of blind source separation, and the basic new tool is the concept of sparsity with respect to suitably chosen collection of signals as a selection rule for modeling. The approach stands to benefit from the theory of sparse representations/compressive sensing which has come to fruition in recent years. Problems of delay estimation, coherence analysis, non-linear and non-stationary modeling are presented with a new angle?seeking relevant information in a jointly-sparse representation of measured time-series. A potentially transformative broad spectrum of tools may result from the new ways of analysis and system identification proposed herein.Broader Impact: The research may impact very different fields such as Physics?in calibrating and filtering measurements, Image analysis?in MRI/medical imaging, System identification, Acoustics and the control of jitter, Communications?blind deconvolution in noisy and resonant channels, Radar processing, and others.