  We propose a unified view of non-local methods for single-image denoising,
for which BM3D is the most popular representative, that operate by gathering
noisy patches together according to their similarities in order to process them
collaboratively. Our general estimation framework is based on the minimization
of the quadratic risk, which is approximated in two steps, and adapts to photon
and electronic noises. Relying on unbiased risk estimation (URE) for the first
step and on ``internal adaptation'', a concept borrowed from deep learning
theory, for the second, we show that our approach enables to reinterpret and
reconcile previous state-of-the-art non-local methods. Within this framework,
we propose a novel denoiser called NL-Ridge that exploits linear combinations
of patches. While conceptually simpler, we show that NL-Ridge can outperform
well-established state-of-the-art single-image denoisers.
