Any image can be represented as a function defined on a discrete weighted graph whose vertices are image pixels. Each pixel can be linked to other pixels via graph edges with corresponding weights derived from similarities between image pixels (graph vertices) measured in some appropriate fashion. Image structure is encoded in the Laplacian matrix derived from these similarity weights. Taking advantage of this graph-based point of view, we present a general regularization framework for image denoising. A number of well-known existing denoising methods like bilateral, NLM, and LARK, can be described within this formulation. Moreover, we present an analysis for the filtering behavior of the proposed method based on the spectral properties of Laplacian matrices. Some of the well established iterative approaches for improving kernel-based denoising like diffusion and boosting iterations are special cases of our general framework. The proposed approach provides a better understanding of enhancement mechanisms in self similarity-based methods, which can be used for their further improvement. Experimental results verify the effectiveness of this approach for the task of image denoising.
['Amin Kheradmand', 'Peyman Milanfar']
A general framework for kernel similarity-based image denoising