Research On Methods Of Image Denoising Based On Total Variation And Shearlet Transform

Image denoising is a key step in image processing, which is decisive for the results obtained by other subsequential processing techniques. The methods for image denoising can be classified as two categories, namely the methods in space domain and those in transform domain. In space domain, the total variation model(TV) has been considered to be one of the most successful and representative denoising models. It has also been widely studied and has many applications. In transform domain, shearlet transform is a “state of the art” method. In this dissertation, we propose a novel total variation model and three shearlet transform based denoising methods and apply them to the removal of Gaussian noise, speckle noise and impulse noise.Our work mainly includes the following aspects:1. We propose a novel total variation model named exponential function(ETV). Furthermore, a fast numerical algorithm is designed for ETV based on Split Bregman algorithm. We apply our ETV on a broad range of standard images contaminated by Gaussian noise, synthetic aperture radar(SAR) image and medical magnetic resonance images(MRI) containing speckle noise, and compared with the related TV, and high-order TV models. The experimental results demonstrate that compared to TV model, our ETV can reduce the stair case effect to a satisfying extent and offer much better trade-off between noise removal and edge preservation than high-order TV models. In addition, ETV also shows a high computational efficiency when boosted by a split Bregman based algorithm.2. We propose an efficient method for salt-and-pepper noise removal based on shearlet transform. We test our method on four images with various noise densities and compare it against seven other efficient methods. Both numerical evaluations and visual quality comparisons demonstrate that the proposed method can achieve significantly improved results in comparison with the other seven methods.3. We also introduce shearlet transform to the removal of random valued impulse noise(RVIN). We proposed two novel methods through comparing and analyzing among five classic RVIN detection methods and combining the more efficient two among them with shearlet transform. And experiments conducted on images corrupted by RVIN with various densities demonstrate that our methods are both numerically and visually more efficient than the five classic methods.To conclude,the work in this dissertation on one hand significantly improves the image filtering methods; On the other hand it also to some extent contributes to the extension and application of the numerical algorithms.