Research On Nonseparable Wavelet Based Image Denoising Methods

With the development of new theories and methods of wavelet and sparse representation over the past decades, image denoising technology has been rapidly developed. This technology makes a great progress in the field of remote sensing image analysis, medical image processing, robot vision, industrial quality supervision, and testing, etc, which leads to the expansion of information science, especially computer vision and intelligent systems. Therefore, the image denoising becomes a research trend in the field of image processing, computer vision and pattern recognition, it is also one of the most important research topics for experts and researchers in related field all around the world. Meanwhile, it has become the key funding field of various national scientific researches.As the characteristics of good locality and multi-scale analysis for the wavelet transform in the spatial and frequency domain, a wavelet-based image denoising research has become a mainstream direction in the field of image denoising. However, as for the issue of complex image denoising, the traditional way has difficulty in solving the wavelet function selectable range, adaptive selection, etc. On the other hand, the current existing wavelet coefficients modeling methods are complex and low efficiency, which restrict practical application. Based on thorough analysis and the principle of wavelet image denoising and the factors of influencing denoising effect, analyticity properties and parameter adaptive selection of nonseparable wavelet, the paper proposes several nonseparable wavelet based image denoising methods, which are listed as follows:1) This paper researches the features of nonseparable wavelet and construction method and answers the question of what parameters of the parameterized nonseparable wavelet filter are the most effective ones to extracted image structure, then proposes the criterion of choosing adaptive wavelet which is based on image itself and parameter selection method of nonseparable wavelets. Nonseparable wavelets not only retain the good locality of the separable wavelet and multi-scale analysis, but also have richer detail informations of the image in high-frequency sub-bands. And the corresponding filter parameters are very sensitive to the structure of the different directions of the image, which contributes to portray the image's non-stationary characteristics effectively. Thus, it is much easier to distinguish the wavelet coefficients corresponding to image structure and noise, which lay a solid foundation for nonseparable wavelet denoising.2) This paper researches the three basic elements of image denoising based SURE-LET, including the choice of the wavelet basis, the confirmation of the threshold function subspace and the calculation of divergence, we use the optimal parameters of the filter to solve the problem of choosing the wavelet basis in the case of nonseparable wavelets. We improve the threshold choice by using cluster with nonseparable wavelet based on SURE-LET, and then focus on analyzing the selection algorithm of the optimal parameters of the filter as well as the approximate method for divergence calculation in SURE-LET. The method can improve the flexibility of the selection of wavelet basis combination, while avoiding the shortcomings of the previous slow calculation. The experimental results show that the method is effective.3) The advantages of nonseparable wavelet are as follows:revealing multi-scale structure, describing the texture structure under different scales, and portraying different directions and different types of singularity structure in a certain extent. On the basis of above merits, we establish a nonseparable wavelet based multi-scale sparse denoising model, and design collaboration sparse models for containing a similar structure component to enhance the stability and accuracy of the sparse representation. The result shows that image denoising effect on the basis of this model improves obviously.The wavelet domain image denoising effect largely depends on the choice of the wavelet basis. By researching the nature of the mathematical analysis of the nonseparable wavelet and filter parameters on repressing the image local structures, this paper researches the criteria and methods of solving the wavelet optimal parameters. Moreover, the paper proposes denoising method, which contains SURE-LET, sparse representation model based on nonseparable wavelet domain. Experimental results show that the above image denoising methods function effectively.