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

盲源分离（Blind Source Separation，BSS）从一个简单的生成模型出发，最小化对数据生成机制的假设，实现对观测数据的有效分解，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（伊卡）一直是最常用的方法来实现BSS，因为在许多应用中，底层组件的统计独立性是合理的。除了独立性之外，样本相关性是许多感兴趣的信号的另一个固有属性。传统上，在开发源分离方法时，这两个属性被分别处理。另一方面，熵率是一种自然成本，它允许人们共同考虑独立性和样本相关性，因此有望产生一类新的具有广泛适用性的强大解决方案。此外，本发明还提供了一种方法，本文的研究重点是发展一类基于熵率的信号源分离和模型选择方法，使之既能考虑高阶信号源，又能考虑高阶信号源，统计信息和样本相关性，以在更具挑战性的问题中实现显着的性能增益。主要的应用领域是一个，可以真正利用这种完全结合的方法：功能磁共振（fMRI）数据的分析和拒绝梯度和脉冲伪影在脑电图（EEG）在并发EEG-fMRI数据。由于这些问题中噪声和伪影的独特性质，这两种应用都已被证明对传统的基于模型的方法具有挑战性。因此，他们提供了一个独特的测试平台的性能评估的新一类的方法，根据这项研究。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，因此这套新方法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.