Image denoising via sparse coding using eigenvectors of graph Laplacian

Image denoising plays an important role in image processing, which aims to separate clean images from the noisy images. A number of methods have been presented to deal with this practical problem in the past decades. In this paper, a sparse coding algorithm using eigenvectors of the graph Laplacian (EGL-SC) is proposed for image denoising by considering the global structures of images. To exploit the geometry attributes of images, the eigenvectors of the graph Laplacian, which are derived from the graph of noised patches, are incorporated in the sparse model as a set of basis functions. Sequently, the corresponding sparse coding problem is presented and efficiently solved with a relaxed iterative method in the framework of the double sparsity model. Meanwhile, as the denoising performance of the EGL-SC significantly depends on the number of the used eigenvectors, an optimal strategy for the number selection is employed. A parameter called as out-of-control rate is set to record the percentage of the denoised patches that suffer from serious residual errors in the sparse coding procedure. Thus, with the eigenvector number increasing, the appropriate number can be heuristically selected when the out-of-control rate falls below an empirical threshold. Experiments illustrate that the EGL-SC can achieve a better performance than some other well-developed denoising methods, especially in the structural similarity index for the noise of large deviations.