Study On Independent Component Analysis Method And Its Applications To Image Processing

Independent Component Analysis (ICA) is a kind of powerful method for Blind Signal Processing (BSP). It becomes more and more important while using in widely fields, such as telecommunications, audio signal separation, biomedical signal processing, and image processing. Many literatures on ICA were published and lots of algorithms were proposed during the past ten years in a large number of journals and conference proceedings. ICA becomes one of the most exciting new topics both in the fields of signal processing and artificial neural networks.In this thesis, the principle and algorithms of ICA are researched in detail. Some modified ICA algorithms by combining ICA with wavelet transform, Self-Organizing Maps (SOM) and BP neural network are proposed, such as ICA method based on wavelet transform, initialization method for post-nonlinear ICA based on SOM, and face recognition method based on ICA and modified BP neural network. Furthermore, the applications of ICA to image processing are discussed, including blind separation of images, feature extraction and pattern recognition, moving objects detection, digital image watermarking and adaptive noise cancelling of images.The main achievements of this dissertation are put forward:(1) A kind of new ICA method based on 2-dimensional wavelet transform is proposed. And this method is used to separate the mixed images. The precision of the Nature Gradient Algorithm (NGA) is discussed by using the error perturbation method. It can be proved that the steady-state error of NGA is inverse proportional to the quadratic of the kurtosis of the sources when the probability distribution function of each source is the same and the nonlinear function is a tanh function. Because the kurtosis of the detail subimages in wavelet domain is always bigger, the separation precision of the proposed method is higher. Furthermore, the size of the sub-image in wavelet domain is a quarter of the source image, so the convergence speed of our method is faster. In addition, the convergence of the FastICA method is analyzed. The conclusion is that the source signals' kurtosis has no effect on the convergence. Because the size of the sub-image in wavelet domain is a quarter of the source image, its convergence speed is faster too.(2) According to the drawbacks of the post-nonlinear ICA method based on SOM, an initialization method with global topology preservation property for SOM network is proposed. The initial weights nearly match with the joint probability distribution of the mixture signals. By using this method, the convergence speed of the SOM network is faster and the algorithm can...