Multiscale hierarchical decomposition in imaging: Progress and challenges

Elena Resmerita (Alpen-Adria University of Klagenfurt)

Abstract: An important problem in image processing is the image restoration one,  that is an ill-posed inverse problem problem which aims to remove noise and blur from a degraded image. An interesting approach in this respect was introduced by Tadmor, Nezzar and Vese (2004, 2008), namely the multiscale hierarchical decomposition method (MHDM). In this presentation, we first consider MHDM extensions to more general ill-posed problems affected by additive noise. Then we show how one can adapt the technique to images corrupted by multiplicative noise and to blind deconvolution problems. Recall that blind deconvolution is a highly ill-posed nonlinear inverse problem, which addresses recovering both the true image and the blur kernel, while little information about the degradation is known. We point out the advantages of the multiscale hierarchical decomposition especially when reconstructing images with features at different scales.