Transform-domain sparsity regularization for inverse problems in geosciences

Sparsity regularization in inverse problems

Algorithms for Imaging Inverse Problems Under Sparsity and Structured Sparsity Regularization

This paper reviews our recent work on the application of a class of techniques known as ADMM (alternating direction method of multipliers, which belongs to the family of augmented Lagrangian methods) to several imaging inverse problems under sparsity-inducing regularization. After reviewing ADMM, a formulation that allows handling problems with more than two terms is introduced; this formulatio...

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...

Regularization and Inverse Problems

An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other deconvolution methods are also discussed within the Bayesian context, focusing mainly on the comparison of Wiener filtering, Massive Inference and the Pixon meth...

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 ...