Nonlocal Total Variation for Image Denoising

A nonlocal total variation (NLTV) scheme for image debluring has already been proposed in the literature. The goal of the present article is to study this scheme in the context of image denoising. We establish that its performance is comparable to non-local means and better than the classical total variation denoising approach. However, we show that the nonlocal total variation scheme is essentially a neighborhood filter and therefore a local one. In order to obtain a truly nonlocal scheme and so as to use redundancy in the whole image, we propose a new energy functional that includes a Fourier term. We call this new scheme spatial-frequency domain nonlocal total variation (SFNLTV). Experiments show that SFNLTV outperforms in most cases non-local means and NLTV algorithms, both in term of Euclidean criteria (PSNR) and visually.