Can images be decomposed into the sum of a geometric part and a textural part? In a
theoretical breakthrough,[Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear …

Total variation methods and similar approaches based on regularizations with ℓ 1-type
norms (and seminorms) have become a very popular tool in image processing and inverse …

Denoising algorithms based on gradient dependent regularizers, such as nonlinear diffusion
processes and total variation denoising, modify images towards piecewise constant …

Multi-scale total variation models for image restoration are introduced. The models utilize a
spatially dependent regularization parameter in order to enhance image regions containing …

We propose a nonsmooth PDE-constrained optimization approach for the determination of
the correct noise model in total variation (TV) image denoising. An optimization problem for …

In the present work, we investigate the inverse problem of identifying simultaneously the
denoised image and the weighting parameter that controls the balance between two …

Motivated by Tadmor, Nezzar, and Vese's work dedicated to multiscale image
representation using hierarchical decompositions, we propose transposing their approach to …

We address the task of reconstructing images corrupted by Poisson noise, which is
important in various applications such as fluorescence microscopy (Dey et al., 3D …

Measurements in nanoscopic imaging suffer from blurring effects modeled with different
point spread functions (PSF). Some apparatus even have PSFs that are locally dependent …

We introduce a locally adaptive parameter selection method for total variation regularization
applied to image denoising. The algorithm iteratively updates the regularization parameter …