Sparsity of solutions for variational inverse problems with finite-dimensional data

Sparsity Based Methods for Overparameterized Variational Problems

Abstract—Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, which may potentially help in bridging sparse approximation based methods to the traditional total-variation minimizat...

Sparsity Based Methods for Overparametrized Variational Problems

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, that has established a very interesting connection between the two, highlighting shown how the traditional total variation mini...

Sparsity-Driven Statistical Inference for Inverse Problems

This thesis addresses statistical inference for the resolution of inverse problems. Our work is motivated by the recent trend whereby classical linear methods are being replaced by nonlinear alternatives that rely on the sparsity of naturally occurring signals. We adopt a statistical perspective and model the signal as a realization of a stochastic process that exhibits sparsity as its central ...

Sparsity regularization in inverse problems

Domain Decomposition Methods for Linear Inverse Problems with Sparsity Constraints

Quantities of interest appearing in concrete applications often possess sparse expansions with respect to a preassigned frame. Recently, there were introduced sparsity measures which are typically constructed on the basis of weighted l1 norms of frame coefficients. One can model the reconstruction of a sparse vector from noisy linear measurements as the minimization of the functional defined by...