Variational Bayesian Approximation methods for inverse problems

Computational and Variational Methods for Inverse Problems

Variational Bayesian Approximation with scale mixture prior for inverse problems: a numerical comparison between three algorithms

Our aim is to solve a linear inverse problem using various methods based on the Variational Bayesian Approximation (VBA). We choose to take sparsity into account via a scale mixture prior, more precisely a student-t model. The joint posterior of the unknown and hidden variable of the mixtures is approximated via the VBA. To do this approximation, classically the alternate algorithm is used. But...

Fall 2015: Computational and Variational Methods for Inverse Problems

Description: This course provides an introduction to the numerical solution of inverse problems that are governed by systems of partial differential equations (PDEs). The focus of the course is on variational formulations, ill-posedness, regularization, variational discretization, and largescale solution algorithms for inverse problems. Students will develop numerical implementations for model ...

A Survey of Direct Methods for Solving Variational Problems

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

Regularized Iterative Stochastic Approximation Methods for Variational Inequality Problems

We consider a Cartesian stochastic variational inequality problem with a monotone map. For this problem, we develop and analyze distributed iterative stochastic approximation algorithms. Such a problem arises, for example, as an equilibrium problem in monotone stochastic Nash games over continuous strategy sets. We introduce two classes of stochastic approximation methods, each of which require...