A Transferred Graph Laplacian Regularization Approach for Color Image Denoising

Image denoising is an ill-posed problem because noise interference during image acquisition frequently leads to serious image degradation. To mitigate this problem, we present a different definition of the normalized graph Laplacian matrix, which consists of a kernel similarity matrix and a related dual random symmetric matrix. Furthermore, we provide the transferred graph Laplacian regularization (TGLR) approach under the manifold structure, which assumes the smoothness of the graph frequencies on the data manifold and promotes the non-local self-similarity property that natural images exhibit. Specifically, the transferred graph Laplacian implicitly encapsulates the graph Fourier basis that interprets image denoising as a graph filtering problem based on data-adaptive Laplacian filters. Finally, an improved steepest descent (SD) algorithm is employed to solve effectively the presented color image denoising problem with symmetry and positive definiteness. Experimental results demonstrate that the proposed approach outperforms several state-of-the-art denoising methods in the objective and subjective qualities.