Nonlinear Diffusion Based Image Denoising In Wavelet Domain

It is said that over 70%information human beings received is obtained through the vision.Images are contaminated by different levels of noise produced in image acquisition and transformation which degrades the quality of images and makes analysis of images more difficult.Image denoising is an important pre-processing task for further processing of image like segmentation,feature extraction,texture analysis etc.The main challenge for image denoising is how to suppress the noise while preserving the edges and other important detailed structures as much as possible.Edge-preserving image denoising has become a very intensive research topic.Traditional Gaussian smoothing is not effective for preserving image edges since the Gaussian kernel is symmetric and orientation- insensitive, resulting in blurring artifact for edges.Wavelet technology and nonlinear diffusion techniques are two recently developed effective image denoising methods.With the characteristic of the two techniques,one associative algorithm is proposed.The fundamental theory of the wavelet is introduced in Chapter Two,including continuous wavelet transform,discrete wavelet transform,Mallat algorithm of wavelet transform and 2D wavelet transform.And then wavelet-shrinkage image de-noising method is also presented.In Chapter Three,with the analysis of the P-M model,it is found out that the anisotropic diffusion model can achieve simultaneous noise reduction and edge preservation. However it is very sensitive to noise.This is mainly due to the fact that the gradient calculation is very sensitive to noise,the noise point may also correspond to large gradient magnitude and be preserved as edge in the diffusion precess.How to reduce the influence of noise on the nonlinear diffusion model has a significant effect to image denoising.And then several improved models are introduced,they are CLMC method,RAD method and Direction Diffusion method. CLMC model is regularized P-M method.The gradients are calculated from a smoothed image,which is obtained by filtering the noisy image at each iteration with a Gaussian kernel.Although the improvement can convert the ill-posed problem in the P-M nonlinear diffusion method into a well-posed one.The problem is that a typical image has a wide variety of edges and it is difficult for one filter to select an optimal scale parameter so as to be adapted to all these edges.For example,a Gaussian filter with a smaller scale parameter can preserve more of the edges,but it cannot smooth the image sufficiently,and noise still has significant influence on the image gradient measurement.On the other hand,using a Gaussian filter with a larger scale parameter for image smoothing,the image can be "regularized" enough,but edges are also smoothed and some weak features may even be removed.As a result,for this kind of regularization method,the calculated gradient magnitudes from the smoothed image may not be able to reflect all true edges in the non-filtered image.So,in both cases,some noisy pixels may be misinterpreted as edge pixels or some true edges may not be detected, and the filtering result may either fail to reduce noise or make the non-detected edges blurred.RAD method improves P-M nonlinear diffusion equation from another perspective.A different monotonically decreasing function is chosen to determine the diffusion coefficient.Compared with P-M method,this method can preserve edges better. While the Direction Diffusion method only smoothes the image point only along the tangent direction of the image edge,with no smoothing at all in the direction orthogonal to the tangent direction,thus to preserve the image edges.Chapter Four is the focus of this study,in which the proposed method,that is Nonlinear Diffusion based Image Denoising in Wavelet Domain,is constructed.Firstly image multi-scale analysis by dyadic wavelet transform(DWT) is demonstrated with a simple example,as shown in figure 4.1.Then the rationale of performing the nonlinear diffusion method in the dyadic wavelet domain is illuminated.Lastly,Numerical implementation of proposed method is presented.Validity of our method is demonstrated by comparative experiment. The main idea of this algorithm is to reduce the influence of noise on the PDE model.Wavelet Multi-scale Analysis provides the noise image with a scale-space representation. After DWT,noise originally in the spatial noisy image is amplified into high frequency information and the noise tends to decrease as scale increases.Thus,at each scale of the scale-space,less noise has influence on the PDE model than that when the PDE model is applied directly to the raw noisy image,gradient calculation is more reliable,better filter result is achieved.With the analysis of both wavelet transform and nonlinear anisotropic diffusion model,The proposed algorithm for noise reduction can be summarized as follows,Stepl Decompose the noisy image into a scale-space with four levels using the DWT to obtain the components(W2j1,d1≤j≤4,(W2j2,d1≤j≤4 and S24d I.Step 2 Apply the Direction Diffusion model in the wavelet domain(W2j1,d1≤j≤4 and(W2j2,d)1≤j≤4 to obtain the denoised components((?)2j1,d I)1≤j≤4,((?)2j2,d I)1≤j≤4.The low-pass component S24d I is kept without doing any modifications.Step 3 Perform the inverse DWT on the denoised wavelet transform components ((?)2j1,d)1≤j≤4,((?)2j2,d I)1≤j≤4 and low-pass componentS24d I to reconstruct the denoised image.Comparative studies demonstrate that the proposed algorithm can significantly improve signal-to-noise-ratio while preserving edges and achieves preferable visual quality.