An Improved Image Denoising Method

There is always a large number of noise in an image.In order to analyze the image better,the pretreatment of image de-noising should be done.The traditional linear de-noising process,e.g.Wiener linear filtering,filters the high-frequency of images. Although the method can achieve the effect of de-noising,it will damage the image details and not perform well on processing the non-stationary signals.Therefore,this thesis utilizes wavelet to denoise the images.The purpose is to eliminate noises,to retain the image edge information effectively,to enhance the image PSNR(peak signal-to-noise ratio),finally to get the reconstructed images clearly.The research thoughts to achieve that goal is: combining the edge detection with improved Bayesian threshold method to denoise the images.In the three preceding chapters of this thesis,we introduce the basic theory of the wavelet transform and its application in image de-noising. The wavelet transform is a new analytical method proposed in the last 20 years.Its main feature is to make certain aspects of issues outstanding by the transform,and consequently, wavelet transform has been successfully applied to many fields, particularly in image processing.The wide application of wavelet theory in image de-noising is primarily attributed to the following characteristics:(1)Nature of low entropy.The sparse distribution of the wavelet coefficients reduce the entropy of the transformed images. (2) Multi-resolution. As a result of the multi-resolution approach, we can very well to describe the characteristics of non-stationary signals, such as the edge of the peak,breakpoint;(3)De-correlation. Because of the wavelet transform can make the de-correlation operation on signals,the noises show a whitening trend,so wavelet de-noising more beneficial than time-domain: (4) Flexibility of base.Because the wavelet transform can choose the transform base flexibly, the application of different occasions for different subjects can choose different mother wavelet function to obtain the best results. The third chapter focuses on the achievements of domestic and foreign scholars in this area,to provide a basis for improving the work of the author below.Although the wavelet denoising method perform better in keeping a image's edge feature than the low-pass filter because of its multi-resolution,the general wavelet methods still make so quite damages to the edge of the image that many of the image information is lost.In order to not only protect the edge of the image but also reduce the noise effectively,this paper presents a resolution:before the threshold shrink treatment,the edge detection pretreatment is completed first,then different treatments to the non-edge and edge wavelet coefficients of the image are made.In order to match with the wavelet thresholding,the paper uses the wavelet edge detection method.The advantage is that, we can directly determine which wavelet coefficients corresponds to the edge of the image features.The wavelet edge detection theory is based on that the first derivative extreme points of the different scale wavelet coefficient correspond to the zero-crossing points of the second derivative and the image signal edge points.When we select the the first derivative extreme points,the noises may be mistaken as the extreme points.Taking the advantage of the Lipschitz exponent thoery,we can pick out the the noises whose rate reduce with the scale increasing.The paper's main work is focused on two improvements on the traditional BavesShrink.The idea is to improve the adaptivity of the threshold shrinking,the theoretical basis is that the energy content is different after the wavelet decomposition. With the increasing levels of decomposition, the wavelet coefficients range increasing, and most energy is on the low-frequency band, while the noises are evenly distributed.Using different, threshold to the different levels can achieve a better result.On the precision scales,the wavelet coefficients should be much big to remove noises effectively.On the coarse scale,the coefficients contains important information,so they should be much smaller to retain the image information. Thus,we can add the factorβto the threshold T,whereβ= (?)lgLj/J, Lj is the length of Jth level. Another improvement mainly lies on a new estimate method for the variance of coefficients.Because in the same subband of Mallat decomposition, the wavelet coefficients associates with the characteristics of poly category, or known as the layer correlation. Even within the same subband the variance of wavelet coefficients of the difference positions differ greatly,therefore,we should divide the coefficients into different regions:the edge points and the non-edge points using the information of edge detection method. The variance of the non-edge point is determined by the adjacent non-edge points wavelet coefficients.These two methods improve the adaptability of the threshold shrink,fulfill the task of denoising effectively.By this theory,the experimental steps can be summarized as follow:(1)Smooth the image f(x,y),the result would still be credited as f(x,y)(2)Detect the edge ,to get the edge points and non-edge points,keep the edge points unchanged.(3)Calculate the edge points to get the threshold,then use the improved BayesShrink.(4)Denoise with soft-threshold function.(5)Reconstruct the image wavelet transform.From the results of experiment, we can see that this denoising method has better smoothing effect,at the same time, details of the features and border information can be kept well,image reconstruction is best. These can be confirmed by the subject (denoising image)and the object(PNRS).