  We introduce a parametric view of non-local two-step denoisers, for which
BM3D is a major representative, where quadratic risk minimization is leveraged
for unsupervised optimization. Within this paradigm, we propose to extend the
underlying mathematical parametric formulation by iteration. This
generalization can be expected to further improve the denoising performance,
somehow curbed by the impracticality of repeating the second stage for all
two-step denoisers. The resulting formulation involves estimating an even
larger amount of parameters in a unsupervised manner which is all the more
challenging. Focusing on the parameterized form of NL-Ridge, the simplest but
also most efficient non-local two-step denoiser, we propose a progressive
scheme to approximate the parameters minimizing the risk. In the end, the
denoised images are made up of iterative linear combinations of patches.
Experiments on artificially noisy images but also on real-world noisy images
demonstrate that our method compares favorably with the very best unsupervised
denoisers such as WNNM, outperforming the recent deep-learning-based
approaches, while being much faster.
