Research On Kernel Regression Methods And Its Application To Image Denoising

Kernel regression method is one of the non-parameteric regression estimation methods, which obtain the estimation from the observation. Because it only needs less information about the image distribution or noise distribution, the method may be widely suitable for all kinds of image and noise processing. And the detail of image may persist while denoising.In the dissertation, under the background of the optical images denoising and synthetic aperture radar image despeckling, the theory and application researches start from the classical kernel regression method. The main work involves the kernel estimation method based on the second derivation and the kernel regression method based on diffusion tensor to improve the kernel function, and the kernel regression method based on p-norm distribution and the kernel regression method based on multiplicative model to improve the fitting model.The main contributions and creativities are as follows:(1) The Kernel Estimation Method Based on the Second Derivation and Its Application to Image DenoisingBased on the classical Nadaraya-Watson estimation, by analyzing the relation between the Nadaraya-Watson kernel estimation and true value, the second derivation of regression function is expressed by the Nadaraya-Watson kernel estimations with the different bandwidths. Then the Nadaraya-Watson kernel estimation is improved to obtain more accurate kernel estimation, and it is the unbiased estimation. Experimental results show that the improved method is feasible and enables us to get regression function that is both smooth and well-?tting. The application of the method to grey image and SAR image indicates that this approach is good to show the detail information in the images.(2) The Kernel Regression Method Based on Diffusion Tensor and Its Application to Image DenoisingBased on the classical kernel regression method, modifying the kernel function with the diffusion tensor, which is obtained by the local structure information from scatter matrix, the kernel regression method based on diffusion tensor is obtained for optical images. Then, using the prior information of SAR image, protecting the point targets by the magnitude information and the edges targets by ROA edge-detect operator, the adaptive kernel regression method based on diffusion tensor for SAR images is proposed. The experiments results show that the proposed method can reduce speckle noise while preserving targets and edges.(3) The Kernel Regression Method Based on p-norm distribution and Its Application to Salt-Pepper Noise ReducingComparing the robustness of classical kernel regression estimation with that of p-norm estimation form the views of influence function and break-down point, the kernel regression method based on p-norm distribution is given, and applied into images with salt-pepper noise. Making use of the image histogram information, the robust kernel regression method based on p-norm distribution is obtained to resist heavy pollution by the salt-pepper noise.(4) The Kernel Regression Method Based on Multiplicative Model and Its Application to SAR Image DespecklingBy analyzing the Essence of the classical kernel estimation under the model of additive noise, the explanation is given from the view of the maximum likelihood estimation. Similarly, the kernel regression method base on multiplicative model is built as the maximum likelihood estimation. And the similarity measure is put up forward based on the Gamma distribution. Considering the multiplicative model for SAR images, the speckle reduction based on the multiplicative model for SAR image is obtained and applied into the SAR images. Experimental results show that the proposed method can reduce speckle noise while preserving targets and edges.