A treatise on independent component analysis in the presence of noise -- simulation and data applications in neuroimaging

Abstract

This doctoral thesis introduces a novel negentropy-based algorithm for model order selection in the presence of stationary colored Gaussian noise in the context of independent component analysis (ICA). Model order selection is a critical step in ICA because overestimation of model order selection may lead to splitting original source components, whereas underestimation may lead to loss of information. The existing order selection methods are prone to overestimation in the presence of colored Gaussian noise. The proposed negentropy-based order selection algorithm is aimed at overcoming this problem. This thesis provides a technical description of the method and reports the results from simulation experiments across a range of data conditions as well as real data applications. The new ICA estimation algorithm, noisyICA, extends the application of Hyvärinen's "fast fixed-point algorithm" for high dimensional data in the presence of white or stationary colored Gaussian noise. The first step of the algorithm is to reduce the dimension of observed data based on the proposed negentropy-based model order selection method. The next step of the noisyICA algorithm is to quasi-whiten data utilizing the noise covariance matrix, replacing the standard whitening procedure. Finally, the algorithm optimizes a contrast function based on Gaussian moments that removes biases due to Gaussian noise. Based on the simulation experiments, noisyICA performed well in comparison with fastICA in terms of bias reduction when estimating an ICA mixing matrix, and provided a reasonable and valid estimation of the ICA mixing matrix. The utility and feasibility of using the negentropy-based algorithm in model order selection is demonstrated in an analysis of two independent fMRI data sets. The first data set came from a task-related fMRI study that observed prescription opiate-dependent patients and healthy control subjects at resting state. The analysis of between-subjects and within-subject conditions demonstrated that the negentropy-based algorithm is consistent and robust to changes in data dimension. The second data analysis utilized the resting-state fMRI data from 25 patients with autism spectrum disorders (ASD). The performance of the negentropy-based algorithm was comparable to other commonly used methods. Finally, resting-state fMRI data from 10 ASD patients and 10 healthy control subjects were compared for brain region activation using group ICA. Brain activation (vision, default mode, and basal ganglia) was better represented for the healthy control subjects than the ASD patients. In sum, noisyICA as an alternative to the existing ICA estimation algorithms is promising based on the simulation analyses. In comparison with fastICA algorithm, noisyICA reduces bias in estimating the mixing matrix of independent components for high dimensional data that contain Gaussian noise.