Bayesian reconstruction of piecewise constant signals

A key challenge in the theory of inverse problems is the derivation of classical methods of regularization from Bayesian formulations. We consider this issue in the context of recovering binary one dimensional functions; think, for example, of the problem of barcode reconstruction from the blurred and noisy signal which comes from the scanner.

This is joint work with Andrew Stuart (University of Warwick) and Viet Ha Hoang (NTU Singapore).

The main ideas of Inverse Problems, Bayesian Method and other concepts would be explained along with the current state of research.