Image Denoising Based On Treelet Transformation

Due to a variety of physical conditions and environmental factors, noise is inevitable when image is acquired, quantized, encoded, transmissed and recovered. To improve the quality of image, we need to suppress the noise in the image and meanwhile preserve the detailed image information in the image as much as possible. Image denoising is of great importance for image pre-processing.This paper introduces a new method for data analysis and processing—Treelet Transformation, which focuses on how to remove image noise and try to keep the details of the original image. The main content can be summarized as follows:(1) A new image denoising method based on Treelet transformation and minimum mean square error estimation (MMSE) is presented. Taking the advantage of Treelet transform in analyzing high-dimensional, noisy and unordered data, an adaptive transformation—Treelet is employed to the similar image patches, with Minimum Mean Square Error applied to estimate the denoised coefficients. After all these referent image patches are processed, those denoised image patches will be aggregated by weighted average, thus producing final denoised image results. With Treelet transform robust towards noise and Bayesian Estimation unbiased and accurate in estimating noise-free coefficients, this method tends to obtain better denoised results. In this paper, a large number of experiments are taken and other classical denoising methods are compared to verify the validity of this algorithm and prove that this method can remove noise in the image as well as maintain good edge features and other details.(2) We propose the image denoising method based on Treelet transform domain and Gaussian scale mixture model. First, image patches with similar texture and structure are classified as the same category, where similar image patches are traced for any image patch of all images. Treelet transformation is applied to the matrix consisting of grayscale values of both current image patches and those similar ones. Then the coefficients after transformation are modeled by Gaussian Scale Mixtures, and Bayesian Least Square Estimation is carried out to calculate denoised coefficients. Experiments show the effectiveness of the method in this chapter. Compared with other methods, this method is good at noise suppression and edge retention, with PSNR effectively improved and better visual results. (3)Another new image denoising method based on gradient edge prior and NSCT Gaussian Scale Mixture model is presented. The gradient edge of the image taken as a priori information becomes part of the energy function, thus controlling the image denoising iteration. With denoised results of the NSCT domain Gaussian Scale Mixture model taken as the initial iteration value, the edge gradient added as a priori information constraints the iterative denoising process. A large number of experiments verify the feasibility and effectiveness of this method. Compared with Non-sampling Contourlet domain (NSCT) Gaussian Scale Mixture model, this method has an advantage of maintaining details and edge information due to the edge gradient information.