Research On SVR Robustness With Its Application In Image Restoration

Support Vector Machine SVM is a general learning approach based on statistical learning theory, which has obtained its practical applications in many areas such as pattern recognition, regression and prediction, and density evaluation due to its excellent generalized capability. When applied to regression and prediction, we often call SVM as support vector regression machine SVR. In general, sample data in regression analysis often contain noise. Therefore, how to determine the optimal parameters such that SVR becomes as robust as possible is an important subject worth of studying. The main aim of this dissertation is to study the theoretical relationships between the SVR's parameters and the noisy inputs.Firstly, the issue of SVR robustness is addressed. Focused on the parameter choice issues of Huber-SVR and norm r-SVR with Gaussian noisy inputs respectively, and based on the Bayesian framework, we derived the two following relationships: (1) with the best robustness, the approximately linear relationship between the parameter μ in Huber-SVR and the standard deviation a of Gaussian noisy input is kept, (2) the approximately inversely linear relationship between the parameter r in norm r-SVR and the standard deviation σ of Gaussian noisy input is kept. Our experimental results confirmed the above claims.Accordingly, on how to recognize pulse noise in image using SVR is investigated. Based on the latest research results on recognizing pulse noise in image using SVM, the two new pulse noise image filters are proposed. One uses SVR to recognize pulse noise, the other combines wavelet transforms with SVC to recognize pulse noise. Experimental results demonstrated the effectiveness of these two new image filters.