We propose a two-step algorithm that automatically estimates the noise level function of stationary noise from a single image, i.e., the noise variance as a function of the image intensity. First, the image is divided into small square regions and a nonparametric test is applied to decide whether each region is homogeneous or not. Based on Kendall's $\tau$ coefficient (a rank-based measure of correlation), this detector has a nondetection rate independent of the unknown distribution of the noise, provided that it is at least spatially uncorrelated. Moreover, we prove, on a toy example, that its overall detection error vanishes with respect to the region size as soon as the signal to noise ratio level is nonzero. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the $\ell^1$ error on the statistics of these regions. Numerical experiments show the efficiency of the proposed approach in estimating the noise level function, with a relative error under 10% obtained on a large data set. We illustrate the interest of the approach for an image denoising application.

We derive a denoising method based on an adaptive regularization of the non-local means. The NL-means reduce noise by using the redundancy in natural images. They compute a weighted average of pixels whose surroundings are close. This method performs well but it suffers from residual noise on singular structures. We use the weights computed in the NL-means as a measure of performance of the denoising process. These weights balance the data-fidelity term in an adapted ROF model, in order to locally perform adaptive TV regularization. Besides, this model can be adapted to different noise statistics and a fast resolution can be computed in the general case of the exponential family. We adapt this model to video denoising by using spatio-temporal patches. Compared to spatial patches, they offer better temporal stability, while the adaptive TV regularization corrects the residual noise observed around moving structures.

Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.