Complex ICA-R Algorithms And Its Application To FMRI

Independent component analysis (ICA) is a high performance signal processing method rised in 1990s. ICA can achieve source separation by only using mixing signals, without knowledge of source signals and mixing matrix. Therefore, ICA has been widely used in communications, biomedical signal processing and other fields. Especially, semi-blind ICA which incorporates some prior information is well developed in recent years and further improves ICA performance to a higher level.However, most of the previous works restrict ICA and semi-blind ICA to analysis of real-valued data, which can not meet the need for separating complex-valued signals. For example, functional magnetic resonance imaging (fMRI) signal is a typical complex-valued mixed signal, and the magnitude and phase of which contain independent information. However, most works only apply ICA to analyze the magnitude of fMRI due to maturity and simplicity of real-valued ICA, which accordingly caused loss of performance. As such, the thesis focuses on how to incorporate prior information into complex ICA algorithms, and on development of complex-valued ICA with reference (ICA-R) under the framework of constrained optimization.The main works are as follows. (1) We examine and implement several complex ICA algorithms such as Infomax, JADE, Cfastica, KM and SUT. (2) We explore methods to incorporate prior information into the blind algorithms based on constrained optimization theory. (3) Within the framework of constrained ICA, we propose a complex-valued gradient-based KM-R algorithm. Simulations results show that the proposed algorithm has much improved performance compared to the blind complex ICA algorithms. (4) We propose a complex-valued fixed-point KM-R algorithm, which retains the desirable properties of FastICA such as cubic convergence without estimation of the sign of kurtosis and adjustment of stepsize. (5) Utilizing the magnitude information about the desired fMRI signal as reference, we apply the proposed algorithm to extract three typical spatial components associated with the task of visual/motor stimuli from the whole brain images data. Results for ICA analyses of real fMRI data show the effecacy of the proposed algorithm.