Collaborative Research: Dynamic Blind Source Separation

合作研究：动态盲源分离

• 批准号: 1027134
• 负责人: Allen Tannenbaum
• 金额: $ 29.99万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1027134&HistoricalAwards=false
• 关键词: Collaborative; Research; Dynamic; Blind; Source

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.

盲源分离（BSS）是指从线性混合物中识别来源的任务。对BSS的传统方法仅限于静态混合物。此外，这种方法通常依赖于难以探索的源统计和非稳定假设。相反，提出的研究通过同时识别动力学和输入源来解决分离动态混合信号的总体问题。制定相关系统识别问题的基本工具是稀疏性的概念，稀疏性用作正规化术语，以自然方式限制输入/过程动力学的选择。拟议的研究将受益于基于1个功能的相当强大的理论，该理论是基于＆＃8467; 1功能的诱导优化的，该理论近年来已经成形。拟议的计划始于对一般的Dynamic-Mixtures-Model分析，Explorings-Modelse，Exploringsparsparsity作为正则术语。此类模型的动机源于系统识别，分布式传感以及光谱分析，子空间识别和天线阵列中的问题。该提案继续进行，概述了专门的形式主义，目的是在类似的框架中捕获延迟/相干分析的问题以及在非平稳/非线性混合环境中的系统识别问题。为此，有人提出关节稀疏性的概念？一种依赖组分 - 分析的形式，是一个合适的工具，用于识别源，谐波等之间的共同点，同时寻求时间表存在和非线性混合的讲述迹象。该提案详细介绍了自回旋动力学的情况，这导致了凸优化问题。噪声，模型顺序和稳定性之间的权衡得到提高，并将其整合到拟议的研究计划中。 BSS和图像分割技术之间的连接是几何BSS的一种形式，它是否以一种为拟议的研究暗示了另一个概念角度的方式。最后，正在讨论字典设计问题，即如何获得合适的？基于先前的信息和可用数据，以确保一定程度的鲁棒性和可计算性的方式，在提高稀疏性的同时，基于先前的信息和可用数据的基础。智能优点：实用和理论问题将在系统动力学和信号传输路径上，在存在的情况下，在存在的情况下，将研究相当无处不在的识别问题。形式主义是在盲目分离的背景下进行的，基本的新工具是相对于适当选择的信号集合作为建模的选择规则的稀疏概念。该方法将从近年来实现的稀疏表示/压缩感知理论中受益。延迟估计，相干分析，非线性和非平稳建模的问题以新的角度？寻求相关信息在共同的时间序列表示中。 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.