Study And Applicat Ion Of Image-denoising By Thresholding Based On Wavelet Transform

Image de-noising is a classic problem of signal processing. Images are influenced easily in the process of digital and transmission by imaging equipment and noise of external environment, become the noisy image. These noise makes the quality of image becomes poor which influence people's understanding of pictures. At the same time, it is related to the effect of subsequent image processing, such as images cutting, target recognition, edge detection and so on. In order to obtain high quality digital image, it is important for de-noising the noisy image, we need to get rid of the useless noise of the signal in the condition of maintaining the original information integrity. So, de-noising algorithm has been being hot research topic in the image processing and computer vision areas. This thesis mainly applies the method of wavelet domain de-noising in the image de-noising.Wavelet de-noising refers to that after the noisy signal being transformed by wavelet; the wavelet coefficients of signal and noise have different characteristics in different scales, constructing the corresponding rules, processing the wavelet coefficients of signal and noise with mathematical method respectively in wavelet domain. The essence of the processing is to reduce or abandon the coefficient completely which noise generated, and keep the original signal wavelet coefficients extremely, finally, to reconstruct original signal and get the optimum estimate of original signal.There are a variety of ways of de-noising based on wavelet transform and the method of threshold de-noising is researched in this thesis. Threshold shrinkage is based on the facts: larger wavelet coefficients almost belong to the actual signal, but smaller coefficients usually are the noise. So by setting the right threshold and wavelet transform, and make the coefficients that smaller than threshold are zeros and keep the bigger ones so that we can achieve the purpose of de-noising. Wavelet transform uses orthogonal wavelet, so it is lack of translational invariance, after de-noising with traditional wavelet threshold will produce visual distortion, namely the pseudo Gibbs phenomenon. Therefore this thesis proposes a method of de-noising algorithm based on static wavelet transform threshold, this algorithm make the signal spread on a group of bases which have'redundance', after static wavelet transform to the signal, make multiple scales equal to the length of the signal, this can solve false Gibbs phenomenon produced by orthogonal wavelet lack of translation invariance, the improved algorithm of de-noising result in all the variance and signal-to-noise ratio is superior to the result of orthogonal transformation. Besides, the traditional threshold de-noising method is not consider the correlation of the scale space, this thesis proposed image threshold filtering algorithm based on the correlation of the airspace domain, this algorithm unions the airspace related de-noising algorithm with threshold de-noising algorithm and make relevant calculation can not only suppress noise at the edge of sharpening signal but also improve signal positioning accuracy of main edges.This thesis uses the method of wavelet threshold de-noising to numerical calculate and simulation experiment, which based on thorough analysis research threshold function and threshold of such necessary parameter selection problem in the process of de-noising. At the same time, this thesis discussed the defects of this kind of de-noising algorithm and proposed two kinds of improved methods. At last this thesis verified the effective of the threshold de-noising method by Matlab simulation experiment and effect analysis.