Image denoising—removal of additive white Gaussian noise from an image—is one of the
oldest and most studied problems in image processing. Extensive work over several …

This paper provides an overview of current approaches for solving inverse problems in
imaging using variational methods and machine learning. A special focus lies on point …

We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators
acting on discrete multicomponent signals. This result naturally leads to the identification of …

We propose to enhance 1-weakly convex ridge regularizers for image reconstruction by
incorporating spatial adaptivity. To this end, we resort to a neural network that generates a …

We propose a regularization scheme for image reconstruction that leverages the power of
deep learning while hinging on classic sparsity-promoting models. Many deep-learning …

Theoretical guarantees for the robust solution of inverse problems have important
implications for applications. To achieve both guarantees and high reconstruction quality …

Image restoration involves solving an optimization problem where the objective function is
the sum of a data-fidelity term and a regularization functional that incorporates a desired …

We present a statistical framework to benchmark the performance of reconstruction
algorithms for linear inverse problems, in particular, neural-network-based methods that …

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-
corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation …

The remarkable ability of deep learning (DL) models to approximate high-dimensional
functions from samples has sparked a revolution across numerous scientific and industrial …