Redefining self-similarity in natural images for denoising using graph signal gradient

Image denoising is the most basic inverse imaging problem. As an under-determined problem, appropriate definition of image priors to regularize the problem is crucial. Among recent proposed priors for image denoising are: i) graph Laplacian regularizer where a given pixel patch is assumed to be smooth in the graph-signal domain; and ii) self-similarity prior where image patches are assumed to recur throughout a natural image in non-local spatial regions. In our first contribution, we demonstrate that the graph Laplacian regularizer converges to a continuous time functional counterpart, and careful selection of its features can lead to a discriminant signal prior. In our second contribution, we redefine patch self-similarity in terms of patch gradients and argue that the new definition results in a more accurate estimate of the graph Laplacian matrix, and thus better image denoising performance. Experiments show that our designed algorithm based on graph Laplacian regularizer and gradient-based self-similarity can outperform non-local means (NLM) denoising by up to 1.4 dB in PSNR.