A Research Approach To Image Denoising Based On Compressed Sensing And Sparse Representations

In the process of acquisition, encoding, transmitting image signal, various noisecontaminates the image inevitably, affecting the quality of image and its subsequentprocessing. In recent years image denoising has received more attention as an importantpart of image pre-processing.Compared with traditional denoising methods, denoising method based oncompressed sensing theory can bring the advantages of sparse representations into fullplay, adapt to actual circumstances flexibly, reduce the sampling rate and the costs ofdata processing, get better denoising results. This thesis based on the sparserepresentation of image, explores and researches Ridgelet transform, Cuevelet transform,overcomplete sparse image representation.This thesis provides the development of image denoising technique and knowledgeof compressed sensing theory, highlights three steps and usual algorithms ofcompressed sensing. Next is the main content:1. All about Ridgelet transform is introduced, especially its research developmentand application and continuous Ridgelet transform, discrete Ridgelet transform, evenRadon transform having a close connection with Ridgelet transform. A new denoisingalgorithm based on Ridgelet shrinkage and total variation minimization model isproposed. Experiment results show this method overcomes the disadvantages ofthreshold shrinkage, has a higher peak signal to noise ratio (PSNR) and a better visualquality, and this method is more suitable for images rich of linear feature.2. The related knowledge of curvelet transform, including two generations of it andexisting problem, is elaborated. Then a new image denoising method based on thenormal Gaussian distribution and Maximum A Posteriori(MAP) estimator is proposed.Via experimental data, this algorithm shows a better performance in image denoising,and preserves the characteristics of the original image better.3. Dictionary and its related theory including propose selection and design of ADictionary are described, knowledge of overcomplete sparse dictionary is elaborated,such as, mathematical description of the dictionary, solution of overcomplete sparse representation. And the irrelevant coefficient of a redundant dictionary is also explained,then two algotithms (greedy algorithm and algorithm for global optimization) aredetailed to solve the problem of optimal sparse representation, the construction anddenoising method of a learning overcomplete redundant dictionary is proposed, thisalgorithm integrates the construction of a dictionary with image denoising, completessparse representation and image denoising simultaneously, finally a comparison isprocessed based on an experiment.