The Application Of Support Vector Machine In Wavelet Packet De-Noising

Image processing has been an active research field as the enhancing capacity of the computer processing and increasing processing demands for the multimedia information in the modern world. The main goal of image de-noising is to improve the image, and make the image meet the real demands.Wavelet analysis is the local time-frequency analysis, which uses time domain and frequency domain to describe the feature of the signal. It is a strong tool for non-steady signal analysis, and it can extract useful information from the signal by multi-scale analysis in detail through expanding and shifting. In recent years, wavelet transform is widely applied in image processing and pattern recognition. Because wavelet transform is linear transform, the wavelet transform of contaminated signal is addition of wavelet transform of signal and noise. In 1994, Donoho proposed image de-noising methods based on soft threshold and hard threshold of wavelet. The basic principle of wavelet threshold de-noising is to deal with high frequency coefficients of wavelet decomposition with certain thresholds according to the feature of the noise wavelet decomposition which always shows as high frequency signal. Following Donoho, many scholars improve these methods through researching the threshold.This thesis provides a new de-noising method based on wavelet packet and support vector machine. The basic steps of the new de-noising method are: firstly the image contaminated by noise is decomposed at all frequencies using the wavelet packet transform. The main goal of this step is to acquire the information of the image in detail; then the coefficients of the wavelet packet decomposition are classified into the original image part and the noise part using support vector machine; finally, the wavelet packet coefficients of the image are reconstructed to recover the image from its noisy version contaminated by noise. The new method uses the cross-validation method to select the parameter of kernel function and penalty factor through analyzing the classifying accuracy and searching time in different searching intervals.The thesis also discusses the application of the new de-noising method to different types of noise, and compares the de-noising effect of the new de-noising method with others'. The result of the simulations shows that the new de-noising method is more effective in preserving the edges of the image, especially in dealing with random noise.