Recovery of shapes: hypermodels and Bayesian learning
Daniela Calvetti, Erkki Somersalo · Journal of Physics Conference Series · 2008
We discuss the problem of recovering an image from its blurred and noisy copy with the additional information that the image consists of simple shapes with sharp edges. An iterative algorithm is given, based on the idea of updating the Tikhonov type smoothness penalty on the basis of the previous estimate. This algorithm is discussed in the framework of Bayesian hypermodels and it is shown that the approach can be justified as a sequential iterative scheme for finding the mode of the posterior density. An effective numerical algorithm based on preconditioned Krylov subspace iterations is suggested and demonstrated with a computed example.