Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

Lasso is a popular method for high-dimensional variable selection, but it hinges on a tuning
parameter that is difficult to calibrate in practice. In this study, we introduce TREX, an …

The aim of this paper was to introduce and study a two-step debiasing method for variational
regularization. After solving the standard variational problem, the key idea is to add a …

In this paper, we propose a new framework to remove parts of the systematic errors affecting
popular restoration algorithms, with a special focus on image processing tasks. Generalizing …

Linear regression relates predictor variables and outcome variables, such as gene copy
numbers and the level of a biomarker. The assumed linearity of the relationships makes the …

In high dimensional settings, sparse structures are crucial for efficiency, both in term of
memory, computation and performance. It is customary to consider ℓ 1 penalty to enforce …

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has
attracted increasing attentions. A large number of experiments as well as some theories …

Sparsity has become popular in machine learning because it can save computational
resources, facilitate interpretations, and prevent overfitting. This paper discusses sparsity in …

Errors-in-variables models in high-dimensional settings pose two challenges in application.
First, the number of observed covariates is larger than the sample size, while only a small …

Bias in image restoration algorithms can hamper further analysis, typically when the
intensities have a physical meaning of interest, eg, in medical imaging. We propose to …