Research On Image Multiscale Geometric Analysis And Its Applications For Image Denoising

Compared with the typical fourier analysis, wavelet transform obtains lots of advantages. Owing to these advantages, it is widely used in various fields of image processing and becomes another important analysis tool.However,wavelet transform only provides an optimal representation for locality and character of signal odd dot and fails to represent the geometic features such as multidirectional edges and textures in 2-dimensional image effectively.In order to search for the optimal image representation,multiscale geometric analysis is proposed and becomes a hot field rapidly.Its theory and application are continuously being developed and perfected.This paper focuses on the applications of multiscale geometric analysis for image denoising mainly.And this paper makes deelply research on wavelet transform, contourlet transform and tetrolet transform in order to design effective and novel image denoising algoithms.The main innovative results in the dissertation are as follows:1. In order to reduce the blocking artifacts resulted from tetrolet transform, which is putted forward by Jens Krommweh, we improve and construct extension to tetrolet transform.The size of every block is changed according to the size of original image. And the new haar transform matrix is obtained from haar wavelet transform matrix recursion function. Moreover, the tetrolet cofficients are reshaped. Some numerical experiments show our method can preserve more significant information of original images, such as edges and details. The proposed method gives better performance in PSNR and visual quality.2. A new uniform thresholding function of waveshrink is build. The new function satisfies the shrinkage condition .By choosing the value of the parameter u , we can obtain an new thresholding function with excellect performances. While the parameter u tends to zero, the new function is similar to the soft thresholding function. While the parameter u is equal to zero, it is the soft thresholding function. At the same time, while the parameter u tends to one, the new function is similar to the hard thresholding function. By changing the parameter u , we can change the trend of this new function. These advantages make it possible to find a flexible method whenever using the wavelet shrinkage method for image denoising. Moreover, computationally efficient formulas for computing bias, variance and risk of the uniform thresholding function are derived. Some numerical experiments show the new function is effective.3. A new adaptive thresholding function is constructed for image denoising .The new function is continuous and has infinite rank continuous derivative. It is suitable for various mathematical processing. At the same time, the new function satisfies the shrinkage condition and it has adaptive character. These advantages make it possible to construct an adaptive algorithm for signal denoising. Moreover, computationally efficient formulas for computing bias, variance and risk of the adaptive thresholding function are derived. Some numerical experiments show the new function can preserve more significant information of original images and gives better performance in PSNR and visual quality.4.A novel image denoising algorithm is obtained by combining tetrolet transform with Stein's unbiased risk estimate approach.Hence, it integrates the advantages of two methods.This approach took advantage of a multi-scale framework and directionality of tetrolet transform to preserve the significant information of original image like edges and details. And Stein's unbiased risk estimate approach denoises a image by minimizing the mean squared error (MSE) between the clean image and the denoised one.It is unnecessary to set a known thresholding. Numerical results show the effectiveness of our technique.5. In this paper, a new uniform threshold function of waveshrink is studied.Two parameters for optimal threshold function are obtained from niche adaptive genetic algorithms. Based on crowding mechanism, punishing function is adopted to adjust individual fitness and advance global capability. We minimize an estimate of the mean square error by using genetic algorithm. Numerical experiments show that the proposed new algorithm is very effective in adaptively finding the optimal solution in mean square error sense.6.Image quality improving techniques based on partial differential equations are famous for the capability of denoising while keeping edges sharp because of the different filters in edges and inner area. Combined with the multi-scale transform, a new image denoising model is proposed with better results for human vision characteristics. The new model has got excellent experiment results of denoising while keeping texture and geometry structure unfading.