CIF: Small: Collaborative Research: Entropy Rate for Source Separation and Model Selection: Applications in fMRI and EEG Analysis

盲源分离(BSS)从一个简单的生成模型出发，最大限度地减少了对数据生成机制的假设，实现了对观测数据的有效分解，因此在信号处理等领域得到了广泛的应用。特别是，独立分量分析(ICA)一直是实现盲源分离最常用的方法，因为在许多应用中，底层分量的统计独立性是可信的。除了独立性，样本相关性是许多感兴趣信号的另一个固有属性。传统上，在开发源分离方法时，这两个属性是分开处理的。另一方面，熵率是一种自然成本，它允许人们同时考虑独立性和样本相关性，因此有望产生一类具有广泛适用性的新的强大解决方案。此外，通过使用信息论准则，可以很容易地将模型选择-补充盲源分离能力的另一个关键问题--融入到该问题中。本研究的重点是发展一类使用熵率的强大的源分离和模型选择方法，使得人们能够同时考虑高阶统计信息和样本相关性，从而在更具挑战性的问题中获得显著的性能改进。主要的应用领域是能够真正利用这一完全结合的方法的领域：功能磁共振(FMRI)数据的分析，以及在并发的EEG-fMRI数据中排除脑电(EEG)中的梯度和脉冲伪影。由于这些问题中噪声和伪影的独特性质，这两个应用程序都被证明对传统的基于模型的方法具有挑战性。因此，它们为这项研究下开发的新方法的性能评估提供了一个独特的试验台。由于独立性和样本相关性是许多其他类型数据的内在属性，新的方法集也将是许多其他问题的有吸引力的解决方案。

Blind source separation (BSS) has found wide use in many disciplines including signal processing as it starts from a simple generative model minimizing assumptions on the data generation mechanism and achieves useful decompositions of the observed data. In particular, independent component analysis (ICA) has been the most commonly used approach to achieve BSS since statistical independence of the underlying components is plausible in many applications. Besides independence, sample correlation is another inherent property of many signals of interest. Traditionally, these two properties are addressed separately when developing methods for source separation. Entropy rate, on the other hand, is a natural cost that allows one to account for independence and sample correlation jointly, and hence promises to result in a new class of powerful solutions with wide applicability. In addition, it enables one to easily incorporate model selection---another key problem complementing the power of BSS---into the problem through the use of information theoretic criteria.The focus of this research is the development of a class of powerful methods for source separation and model selection using entropy rate so that one can take both the higher-order-statistical information and sample correlation into account to achieve significant performance gains in more challenging problems. The main application domain is one that can truly take advantage of this fully combined approach: the analysis of functional magnetic resonance (fMRI) data and the rejection of gradient and pulse artifacts in electroencephalography (EEG) in concurrent EEG-fMRI data. Both are applications that have proven challenging for the traditional model-based approach due to the unique nature of the noise and artifacts in these problems. Hence, they provide a unique testbed for the performance evaluation of the new class of methods developed under this study. Since independence and sample correlation are intrinsic properties of many other types of data, the new set of methods will be attractive solutions for many other problems as well.