Abstract
Image patches are considered as the fundamental building blocks of an image. In this dissertation, the restoration of a noisy image based on its redundant patches is studied. Nonlocal means (NLM) is known as a weighted average filtering based on patch similarity. We propose to improve NLM by only including a cluster of pixels with mutually similar patch appearances to that of the pixel to be denoised. A coalitional game model is designed to find an optimal cluster of pixels for every noisy pixel. In the coalitional game model, each pixel is treated as a player and each player receives a payoff which depends on the mutuality among players in the same group. Therefore, pixels with similar patch appearances are prone to group together for cooperation. We propose betrayal and hermit rules to describe the cooperative behaviors among the players and apply it to find the optimal and stable group of pixels for the denoising purpose. In addition, stability analysis of our coalitional game model is given. Besides, we propose an alternative patch-based approach, which suppresses the image noise by shrinkage of coefficients in transform domain. We first sample overlapped patches from the noisy image and then cluster them into many similar groups. For every group of noisy patches, we apply probabilistic principal component analysis (PPCA) to denoised jointly in the learnt PCA domain. Putting back the denoised patches to their original positions, the denoised image is then reconstructed. Our two patch-based denoising approaches are shown to be effective in removing the image noise while maintaining the edge structures of the original noise-free images. The superior performances are shown by both visual and quantitative qualities.