Study Of Image Denoising Based On Independent Component Analysis

Recently, theories and methods of signal processing are obtained to develop quickly. There are many kinds of methods in signal processing domain. Independent component analysis (ICA) technology is an effective theory and method in signal processing fields. Its developing tends gradually to maturity and systematization. ICA aims at recovering the latent variables (sources) only from the observed mixtures. It is a generalization of Principal Component Analysis (PCA) that separates the higher-order dependencies in the observed mixtures, in addition to the second-order dependencies. Compared with the other methods, the independent components of ICA are both nongaussian and statistically independent. It is well know that, in the field of image analysis and pattern recognition, much of the important information of the images may be contained in the higher-order relationships among the image pixels. ICA based on higher-order statistics, has shown great promising ability in image feature extraction and image compression.This thesis presents the theories and algorithms of ICA and explores its applications in the image feature extraction, image de-noise and face recognition. The main work of the author focuses on the following aspects:1. Firstly, the paper gives an overview of the status of ICA research.2.The paper introduces some ICA-related knowledge:statistics and information theory. It elaborates pretreatment process of ICA and the condition of completing ICA. The comparison of ICA and PCA is elaborated in the paper.3. This article analyzes some basic criteria and the common methods of ICA from definition and supposition condition. Several kinds of optimized algorithms to objective function in ICA are proposed.4. The article has also quoted the wavelet threshold denoising and denoising based on mathematics morphology method in order to explain fully superiority of independent component analysis in denoising.Wavelet analysis is internationally recognized up to the minute tool for analyzing time frequency. This paper discusses the technique of image processing based on wavelet transform. Wavelet has been well acknowledged to an important method in image denoising. According to make an analysis of wavelet image denoising, four ways based on wavelet threshold denoising are described, tough- threshold denoising,soft- threshold denoising,nonlinear threshold denoising. The experiments show that these methods have an excellent effect to elimination incisive noise. Mathematics morphology theory and method is used in noise pollution image processing.Series and parallel compound morphology filter of opened and closed operation is structured. Multi-structural element is carried on processed to eliminate completely noise in morphology filter process. Experiment indicates these methods not only effectively suppress noise in image, but also preferably maintain image primary geometry characteristic.5. The image data and noise are mutual independent. ICA is applied to obtain the statistic information from noise-free images, and removes the independent noise from noise image using the statistic information. The image data and noise are mutual independent. ICA is applied to obtain the statistic information from noise-free images, and removes the independent noise from noise image using the statistic information. Firstly, denoising method based on mathematics morphology is used in eliminating noise in this paper. It is taken as the reference model which doesn't noise. Secondly, the sparse code contraction is utilized in image processing. The concrete step is that conversion matrix can be obtained though FastICA. The contraction function is received according to the base vector rule. The image vectors including noise are projected though transformation matrix. The projection vectors are eliminated noise with contraction function. Finally, denoising images are obtained according to ICA inverse transformation. ICA could maintenance the original image information better than general denoising methods.6. This paper discusses maximization of non-Gauss, minimization of mutual information and Informax to substitute the sparse code in the paper. Regarding to maximization of non-Gauss, the paper has already said that sum of the independent distribution variable tends to the Gaussian distribution according to the law of averages. Comparing to these independent variables, sum of several independent components must approach to Gauss distribution. It can extract independent component as long as the closest Gauss's variable having not been extracted. There are two methods in measuring non-Gauss. One is kurtosis the other is negative entropy. It is the algorithm based on negative entropy in the paper. Infomax has close relation to MLE. That to say, this method is equal to MLE. Therefore the article has also selected optimization algorithm of MLE. Nonlinear PCA is proposed and use in ICA by Karhunen and Oja. It is approximately same with theory frame criterion under the information. The key of algorithm is the choice of nonlinear function. The choice of function is concerned with the extraction source which is Asian Gauss or Ultra Gaussian as well as the treats parameter which decides. In the optimized algorithm aspect, the paper selects the algorithm of least-squares which the speed is relatively quick. Sparse coding method is used in this paper. FastICA algorithm is used in extracts sparse components. This limit is reasonable to sparse variables. Because of the application of image processing in the paper, its distribution is sparse. The simulation results obtain Basis vectors which several algorithms extract and it shows the proposed method has sparser and faster convergence than others.