In this talk, two denoising algorithms to deal with the additive white Gaussian noise model are described. In the line of work of the Non-Local means approach, we first present an adaptive estimator [1] based on the weighted average of observations taken in a neighborhood with weights depending on the similarity of local patches. The idea is to compute adaptive weights that best minimize an upper bound of the pointwise L2 risk. We show that the " oracle " weights are optimal if we consider triangular kernels instead of the commonly-used Gaussian kernel. Furthermore, we propose a way to automatically choose the spatially varying smoothing parameter for adaptive denoising. The implementation of the proposed algorithm OWF [1] is straightforward and the simulations show that our algorithm improves significantly the classical NL-means and is competitive when compared to the more sophisticated NL-means filters both in terms of PSNR values and visual quality.

In the second part of the talk, I will present another statistical aggregation method [2], which combines image patches denoised with conventional algorithms. We evaluate the Stein’s Unbiased Risk Estimator (SURE) estimator of each denoised candidate image patch to compute the exponential weighted aggregation (EWA) estimator. The resulting PEWA algorithm [2] has an interpretation with Gibbs distribution, is based on a MCMC sampling and is able to produce results that are comparable to the current state-of-the-art. We also demonstrate the performance on fluorescence microscopy images corrupted by Poisson-Gaussian noise.

[1] Q. Jin, I. Grama, C. Kervrann, Q. Liu. Non-local means and optimal weights for noise removal, SIAM Journal on Imaging Sciences, 10(4):1878-1920, 2017

[2] C. Kervrann. PEWA: Patch-based Exponentially Weighted Aggregation for image denoising. Proc. Neural Information Processing Systems (NIPS’14), Montreal, Canada, Décembre 2014