Research On Independent Component Analysis Algorithmand Its Applications To Signal Processing

Independent component analysis (ICA) developed in1990s is a multivariate statistical and computational technique. Its basic task is to separate or extract independently hidden components that underlie sets of random variables, measurements or signal mixtures. ICA can be considered an extension to principal component analysis (PCA) and factor analysis (FA). In contrast to PCA and FA, ICA is a more powerful technique, which can reveal the underlying components or factors of the observed data when these classical methods fail completely. ICA defines a generative model for the observed multivariate mixtures, which are often given as a large database of samples. In the ICA model, the observed data variables are assumed to be linear or nonlinear source signal mixtures. In fact, neither the original sources nor the mixing system is known in advance. The latent variables are called the independent components of the observed data, which are assumed non-Gaussian and mutually independent. These independent components, which are also called source signals or factors, can be separated or extracted by ICA methods.Recently, blind source separation (BSS) and blind source extraction (BSE) on the basis of ICA have received much research attention due to their potential applications in the fields of speech processing, biomedical signal processing, image feature extraction and wireless telecommunication system, etc. Much effort has been devoted to the development and application of BSS/BSE methods. As a result, there are some progress in ICA theories and applications. However, ICA is still in an initial stage of development and many unsolved problems about its theory and application still exist, which restrict its development and application. In general, ICA technique needs to be further enhanced and improved.In this dissertation, we first briefly introduce the development history and the current research status and applications of ICA both at home and abroad. Then some mathematical preliminaries in ICA technique are provided, including the mathematical definition of ICA, the assumptions made about ICA problems and the mathematical theories and methods currently used in ICA, etc. At last, some problems of extended ICA (for example, the blind extraction of desired temporally correlated signals, noisy component extraction on the basis of Gaussian moments and reference signals, and blind source extraction on the basis of the normalized kurtosis value range of the desired signal) are investigated deeply and several efficient algorithms are introduced.The main works in this dissertation can be introduced as follows:Based on the maximum likelihood estimation (MLE) technique and the assumption that the desired source signal is temporally correlated, a reliable method is proposed for blind extraction of temporally correlated signals from linear mixtures. The problem of blind source extraction for temporally correlated signals (TBSE) is an extension of standard ICA. Since majority of measurements obtained from biomedical applications exhibit some degree of periodicity, TBSE technique will have widely potential applications. The existing BSE methods for temporally correlated signal mixtures have many limitations such as computation-demanding and imprecise estimation. To help mitigate these limitations, we propose an improved TBSE method.In practical applications, the conventional TBSE methods may have many problems associated with the measured recordings. For example, temporally correlated relations are not strictly satisfied. Although the desired signal is strongly temporally correlated at a specific time delay, sometimes it also weakly temporally correlates with other source signals or noise. Furthermore, some of other source signals may be also temporally correlated at the same time delay. Therefore, the extracted signal is often contaminated by some undesired signals or noise. Maximum likelihood estimation (MLE) is a fundamental technique of higher order statistics (HOS) estimation. If the source signals are not Gaussian and time dependent, MLE can be efficiently utilized to develop BSE methods. The MLE based BSE algorithm can extract the underlying signal from source signal mixtures. Due to local maximization and random initialization, the signal extracted by MLE based BSE algorithm often converges to a local maximum, which is not necessarily the desired one. To extract the desired signal from the observed signal mixtures exclusively, we propose a hybrid algorithm by combining the TBSE technique and the MLE technique. The whole extraction procedure is divided into two stages. In the first stage, period property of the original source is employed to extract the desired signal from its linear mixtures. However, the extracted signal is often mixed with some undesired signals or noise, so this stage can only be considered to be a rough extraction process. In the second stage, further extraction is accomplished under a maximum likelihood framework by introducing a parametric density model and exploiting the statistical independence of the source signals. This model is constructed with an exponential power family of density functions. As these functions can adaptively match the source marginal probability densities, the signal obtained in the first stage can be further processed without any precise knowledge of the source probability distribution. As a result, the extracted signal is stable and efficient. Computer simulations on biomedical signals confirm the effectiveness of the proposed algorithm. Further comparison with other algorithms in existence verifies its reliability and robustness.In contrast, BSE has many advantages over conventional BSS method such as the low computational load and fast processing speed. Therefore, BSE has been widely used to solve blind signal separation problem where there are a lot of source signals while only one or a few are desired. In practice, the desired signal is always contaminated by other signals or noise. For example, measured biomedical signals are seldom recorded in isolation and are almost certainly contaminated by other signals or noise. Noise often results in wrong clinical diagnosis. Sometimes incorrect interpretation of noise may lead to death.As an important non-Gaussian measuring index, the normalized kurtosis has been wide utilized as the objective function for BSS/BSE problem. Despite of being theoretically well justified, vast majority of the existing normalized kurtosis based methods are conducted in noise-free environment, which is not realistic in practice. Recently, a few source extraction algorithms have been proposed on the basis of normalized kurtosis to extract a desired source signal from noisy mixtures. However, most of these algorithms need to obtain a specific normalized kurtosis value of the desired signal in advance. In real world, we often meet with cases that although the precise normalized kurtosis value of the desired signal cannot be obtained in advance, we are blessed with some foresight that the normalized kurtosis of the desired signal generally lies in a specific value range while other unwanted source signals do not belong to this range. By now, it seems that no existing BSE algorithms can be utilized for such cases in noisy environment.A new objective function on the basis of normalized kurtosis is introduced in this dissertation. Maximizing this objective function and adopting Lagrange multiplier method, a robust BSE algorithm is developed which can extract the desired signal as the first output with coarse estimation of its normalized kurtosis value range. If one knows that the normalized kurtosis of the desired signal lies in a specific value range, whereas other unwanted signals do not belong to this range, he can extract the desired signal with the proposed algorithm from its mutually independent mixtures in noisy environment even if sometimes the normalized kurtosis values of different signals are very approximate.In many BSS/BSE applications, especially for biomedical signal processing problems, one may obtain some prior information (e.g. the morphology, the phase, the trace and the occurrence time) about the desired signal in advance. If such prior information, which is closely related to the desired signal, carries enough valuable information to efficiently distinguish the desired signal from the observed signal mixtures, it is called the reference signal. In general, the reference signal is always considered to be the closest one to the desired signal in terms of a proper closeness measure.Nowadays, several BSE methods have been developed by using the reference signal. Lu et al. proposed a good candidate called ICA with reference (ICA-R) or constrained ICA (cICA) for extracting a source signal from a large number of signal mixtures. ICA-R is constructed by minimizing the less-complete objective function and making the best of traces of the desired signal. By incorporating traces of the desired signal into the famous FastICA algorithm, ICA-R may extract the desired signal, which is the closest one to the reference signal. As a classical BSE algorithm for exploiting the reference signal, ICA-R has been sucessfully used in the field of functional Magnetic Resonance Imaging (fMRI). However, ICA-R does not take into account the existence of noise and cannot work well in many cases due to the existence of noise.The reference signal carries enough prior information to distinguish the desired signal from signal mixtures exclusively. In practice, the desired signal is often contaminated by noise. An improved BSE algorithm on the basis of the reference signal is proposed for extraction of the desired signal from noisy measurements. We incorporate the reference signal as an additional constraint into a noisy objective function so as to form a constrained optimization problem. According to the Lagrange multiplier method and the gradient optimization technique, we develop a new BSE algorithm on the basis of the reference signal which can work well even in noisy environment. Computer simulations confirm the effectiveness and reliability of the proposed algorithm.