Source Adaptive Independent Component Analysis Algorithm And Its Application

Independent component analysis (ICA) is a new direction in the signal pro-cessing fields which was developed in the 1990's, and it is one of the most ef-ficient method for solving blind source separation (BSS) problems. ICA is notonly widely applied to the fields of sound signal processing and image process-ing, it has also demonstrated to be successful in various fields such as electro-cardiographic (ECG) processing, electromyography (EMG) processing, magneto-encephalograms (MEG) processing. This dissertation is devoted to the study ofICA algorithm and its application. Several adaptive ICA algorithms are proposed.At the same time, ICA is applied to denoise the sound signal and image data. Themain contributions of the dissertation are as follows.1. After the analysis of the advantage and disadvantage of some traditionalICA algorithms, we propose an ICA algorithm through solving the gradi-ent equation. To solve the gradient equation, an iterative method based onNewton's method is proposed where no learning rate is needed. Meanwhile,this method is very simple because the iterative equation can be obtained bymeans of solving a linear equation, which makes the algorithm very ease touse. At the same time, nonparametric density method is used to estimate theprobability density functions of the sources as well as their first and secondderivatives, which makes the algorithm adaptive to the source distributions.2. A modified kernel density method is proposed to overcome the high com-putation cost of the standard kernel density method especially when thedata size is very large. This modified kernel density method utilize the his-tograms of the sources to directly estimated the parameters of the kernel func-tion. Thus the computation speed is faster than the standard kernel densitymethod especially when the data size is very large.3. In general cases, the demixing matrix in ICA is not in the standard Euclideanspace but in the Riemannian space. Thus the tradition gradient direction is not the speedest direction. To obtain the speedest direction in Riemannianspace, we start from the viewpoint of natural gradient (or relative gradient)to derive two forms of natural gradient by means of invariant rule of theLie groups. Two forms of estimating equation are proposed based on thetwo forms of natural gradient. The source adaptive ICA algorithm can beobtained by solving the estimating equation iteratively where the probabilitydensity function is estimated adaptively. The algorithm based on solving theestimating equation has the property of superefficiency which can reach theFisher efficiency since the steepest direction is obtained by natural gradient.4. After introducing the whitening pre-propessing, the demixing matrix mustbe orthogonal. Under this constraint, the learned demixing matrix must bere-orthogonized after each step, which leads to a fixed-point ICA algorithm.The computation complexity of the fixed-point algorithm is low, and the con-vergence speed is fast.5. The ICA algorithm is applied to denoise the sound signal and image data. Theindependent components of the noisy signal is obtained by ICA algorithmand the noise is removed in the independent component domain, and thedenoised signal is obtained after the inverse transform.