Patch-based Image Restoration Algorithm

Image is one of the most important information media. Only clear image can assure theinformation fidelity. However, many inevitable factors can introduce image deterioration in itsforming or transmission. Hence, the restoration of clear image from degraded one isindispensable. Research on image restoration is of great significance due to its wideapplications in many areas, such as medical image processing, meteorological remote sensing,biological identification, security monitoring and target tracking.Compared to the pixel-based algorithm, recently patch-based image restoration algorithmshows a strong advantage, but few people analyze their algorithm from the perspective ofpatch distribution. In view of this, two image de-noising algorithms are proposed in this studyaccording to the impact of noise in patch distribution. The main work and research results areas follows:(1) The image patches distribution characteristics is analyzed. By observing twodimensional and higher-dimensional image patches distribution, patch manifold is verified. Itis checked that the self-similarity of image patch correspond to the local density of patchmanifolds, the fewness of patch types in an image correspond to the global sparsity of patchmanifolds. Manifold compactness consists of local density and global sparsity.(2) The impact of degradation factors in patch distribution is analyzed. It is showed thatthere is no intuitive influence of motion blurring on patch manifolds. And it is showed thatnoises make an image’s patch manifolds loose. So de-noising can achieve by compact imagepatch manifolds. According to the above observations, two de-noising algorithms based onpatch manifold recovery are proposed. They are named as Block Matching Means (BMM)and Block Matching Robust Principal Component Analysis (BMRPCA), respectively.(3) BMM is simple and easy to understand since it is directly derived from patchdistribution. BMM surpass NLM in terms of de-noising performance, especially in the case ofhigh level noise.(4) BMRPCA performs better than the algorithm using classical principal componentanalysis by employing robust principal component analysis to restore manifolds. The impactof the origin’s location on principal component analysis is also investigated. A further mathematical definition of manifold compactness is expected in the future, sothat image de-noising can be formalized into manifold compacting.