Research On Image Quality Improvement Based On Partial Differential Equations And Calculus Of Variation

Images, during the courses of formation, transmission, storage and processing, will inevitably import some distortion because of imaging equipment limitation, imaging condition interference, image transmission channel noise and compression, etc. The degradation of images exist abroad in remote sense, medical images, surveillance images, fingerprint images, etc. These have made image quality improvement one of the most important and basic problems. Along with the increase of application requirement and technology development, image processing based on partial difference equations(PDE) and calculus of variation(CoV) are gaining importance for their excellent performance. In this thesis, we have made research systematically and thoroughly on image quality improving techniques based on partial difference equations and calculus of variation. Our main work are summarized as follows:1. Nonlinear diffusion filters based on PDE are famous for the capability of denoising while keeping edges sharp, but the problem of smoothing out the image details also exists, and meanwhile the traditional analysis methods are complicated. We first present an analysis method of adaptive iterative convolution(AIC) system, which lay emphasis on the adaptiveness of these algorithms and avoid complicated theory derivation. A class of nonlinear diffusion filters with feature preserving characteristics can be proposed based on AIC. Corners, being an important image feature, are gradually smoothed out and eventually vanish in the process of traditional nonlinear diffusion. According to AIC, we add a curvature term to the diffusion coefficient and get a new filter which could denoise and keep edges and corners sharp. We also do study to the influence of incorrectness of gradient denoting orientation to nonlinear filtering. Comparing several orientation estimation methods, we propose to use the tensor orientation estimation results for filtering and get better denoising results.2. Image quality improving techniques based on variational energy minimization has also got quite great development. We summarize its development and main models, experiment using finite difference method and finite element method both, derive the finite element method formulations, solve the sparse matrix correction problem from boundary extending. Image quality improving techniques based on variational energy minimization can also be used in image restoration. Combined with the Weber's law, a new image restoration model is proposed with better restoration results for human vision characteristics. Image decomposition model is also studied in this thesis. Using image decomposition model, a new texture preserving variational energy minimization model is proposed to solve the problem of texture smoothing in traditional filters. The new model has got excellent experiment results of denoising while keeping texture unfading.3. Image inpaiting can been considered as a special image quality improving problem. We summarized the thoughts in professional manual inpainting, combining the thoughts in Adaptive Iterative Convolution system, and we propose a new image inpainting model based on Mean Curvature Motion(MCM). Compared with classical image inpainting algorithm like BSCB and TV etc, the new algorithm could get better inpainting results, especially for images with high contrast edges damage, and also less complexity. We also propose a new quantity to substitute traditional curvature term and applied to CDD model, experiments show better results. We also propose a new inpainting algorithm based on image decomposition. It has got a smaller region for texture synthesis and a smaller region to search for the best texture block, and thus needs less time, with the same good inpainting results.