The Research Of De-noising Method Based On Curvelet Transform

In the past several years, wavelet transform has been used widely in image processing. Because wavelet transform owns the advantages of time analysis and frequency analysis, and it has the near-ideal ability to represent one dimension or second dimension function for dots singularity. But wavelets theory is only appropriate in describing the image with isotropic singularity, it can't make full use of geometrical characters of the objects, such as, the main characters are edge or contour for second dimension image, and the main characters are the aspects that people are most interested in. Curvelet transform is a very suitable method for describing the image with anisotropic singularity. In high dimension situation, it can effectively describe the directional singularity in the image and suitable for the image with anisotropic singularity characteristic, curvelet transform also has the same ability of local time-frenquence analysis as wavelet transform.Compared with wavelet, curvelet transform not only has excellent characteristics of multi-cale, spacial domain and frequency domain but also has multi-direction which can represent the edge directions of all image exactly and has the greatest near-ideal ability. It represents the edges and smooth regions of an image greatly. At present, curvelet transform has been used widely in image processing.In this paper, three methods are introduced based on wavelet transform de-noising, they are respectively for wavelet shrinkage method, modulus maxima method and correlation method. The advantages and disadvantages of these methods are compared. The wavelet shrinkage method is mainly discussed. An analysis of the choice of threshold, threshold function and some parameters in the process of de-noising is made in detail, and then some common choice grounds are given. The paper introduces the defines and the implementation procedure of the first generation curvelet transform and the second generation curvelet transform in detail, and main properties, coefficients characteristics and sparsity of the curvelet transform are also mentioned. The traditional thresholding function method in denoising can appear some bad phenomenon. For example, the hard-thresholding function results in Pseudo-Gibbs phenomenon, soft-thresholding function can make the image too smooth. Based on the above, the research of this thesis consists of two aspects: One is the improvement based on the hard-threshold function. Then applied it in curvelet transform image de-noising, the experiments show that the de-noising results not only have been improved in wavelet transform but also in curvelet transform;The other is that we combine the cycle spinning with the second generation curvelet tansform for image de-noising. The improved garrote thresholding function is used during the de-noising process. To investigate the effectiveness of the proposed image de-nosing method, we applied the proposed method on three standard images in the experiments. Different standard deviation is added to the standard image. The results are compared in three aspects. They are respectily for the PSNR of the de-noisied images, the de-noisied image and the curve trend of the PSNR. The results of the experiments show that the method proposed in this paper improves the PSNR of the images. The new method can inhibit "Peendo Gibbs" effect to some degree and can also preserve more image details, it usually obtains better performance.