INV

Abstract

We consider the inverse problem of estimating a function $u$ from noisy measurements of a known, possibly nonlinear, function of $u$. We use a Bayesian approach to find a well-posed probabilistic formulation of the solution to the above inverse problem. Motivated by the sparsity promoting features of the wavelet bases for many classes of functions appearing in applications, we study the use of the Besov priors within the Bayesian formalism. This is Joint work with Stephen Harris (Edinburgh) and Andrew Stuart (Warwick).