Contourlet Transform And Its Appliation On Image Denoising

Most of the natural images are the noisy images, when the noise is serious, it will affect the image segmentation, recognition and understanding. The traditional image denoising method will make the image details become blurred. Since the wavelet transform is a role of "mathematical microscope", it can preserve the image details while denoising and restore the original image in the best way. Different from the one-dimensional piecewise smooth signal, the natural image signal whose discontinuous points (for example, the edge) range along the curve (for example, contour lines). 2D wavelet transform can capture effectively of those discontinuous points, but they can not effectively express the arrangement of these points. For the two-dimensional images, the direction information is a very important feature, however, the 2D wavelet transform has limited directions, it can not express all the directions of the images. Because of these disadvantages, the wavelet transform is not appropriate for image sparse expression.In 2002, M. N. Do and Vetterli M. pioneered a sparse representation for two-dimensional piecewise smooth signals that resemble images-Contourlet transform, which is good at capturing the geometric structure of images. It has overcome some inherent limitations of wavelet in capturing the 2D singularity. It is a 2D smooth signal sparse representation. Contourlet transform is a novel image multiscale geometrical analysis method, is a new image decomposition scheme, which provides sparse representation at both spatial and directional resolutions.It offers a flexible multiresolution and directional decomposition for images, since it allows for a different number of directions at each scale.Contourlet transform is the extension of 2D wavelet transform using multiscale and directional filter banks, and leads to a flexible multiresolution, local, and directional image expansion using contour segment. It is good at isolating the smoothness along the contours., capturing the edges of images. The Contourlet transform can get the sparse expression of image and edge smoothness. It will be widely used in digital image processing in the future. In this paper, we mainly discussed the Contourlet transform and its application in image denoising. Main innovative contributions are as following:1. The theory and implementation of Contourlet transform and its application on image processing are discussed. We proposed to adopt the generalized Gaussian distribution to fit the Contourlet coefficients. Also we discussed the disadvantages of Contourlet Transform, further more, we believed that the Contourlet transform will be widely used in digital image processing in the future.2. The theory of image denoising by thresholding based on wavelet transform is studied, because of the disadvantages of wavelet transform, a method for image denoising based on Contourlet Transform was proposed. Making use of the Contourlets'good directionality and anisotropy, we can get better denoising results. As Contourlet Transform can expressed the image edge features better than wavelet transform, it can protect the edge of the image features and texture information better, the denoisde images will be more clear and fits to visual performance. The Contourlet coefficients are divided into two kinds: the first kind coefficients are getted from the noise included in the images, usually, they are abandoned; The second kind coefficients are made up of the 2D anisotropy characteristics of the images, they are preserved or amend.3. This paper summarizes the various image denoising methods, and they are compared. Also proposed the advantages and disadvantages of the thresholding functions, As we know, the hard thresholding and soft thresholding function are discontinuous, there is deviation between the original coefficients and the estimated coefficients, so we combine the hard thresholding function with the soft thresholding function, to get rid of the disadvantages, we combine the two functions together. The new thresholding function to some extent overcome the shortcomings of the hard and soft thresholding functions. The Contourlet thransform provides sparse representation at both spatial and directional resolutions, It offers a flexible multiresolution and directional decomposition for images, since it allows for a different number of directions at each scale. On this basis, we poposed a multiscale and multidirectional image denoising algorithm based on Contourlet transform, We adopt different thresholdings on different scales and different directions. Experiments results show that this method improves the SNR on a certain extent, to a certain extent, also makes the denoised image more clear and fits to visual performance, the texture of images are preserved effectively.4. Yu-fei and so on proposed a Multi-Threshold shrink image denoising method based on wavelet transform. The wavelet transform is the best when analysis of the transient characteristics of singular points. However, it is not optimal when analysisof the anisotropy of straight lines or curves. Because of the disadvantages of the wavelet transform, we proposed the Multi-Threshold shrink image denoising method based on Contourlet transform. The selection of the optimal threshold based on Bayes theory, we believed that the Contourlet coefficients are subordinate to the GGD (generalized Gaussian distribution). Experiments results show that Contourlet Transform can be used to get better image denoising results. It not only improves the signal-to-noise ratio of the images, the denoised images are clearer, but also improved visual effects, can get the better objective and subjective result at the same time.