arXiv subjects
Publications and source records attributed to J. Zubelli.
We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). Our goal is to extend the recent convergence results for the Landweber-Kaczmarz method obtained in [Haltmeier, Leitao, Scherzer 2007], in order to derive a convergent iterative regularization method for an inverse problem in MRI.
We gave a new very simple proof that the completion of the space of the diffeomorphism of the circle modulo conformal maps with respect to the Weil-Petersson Metric is a complex analytic manifold modeled on the Hilbert space with 3/2 Sobolev norm. Our proof is based on the analogue of the Hadamard Theorem that the exponentila map is a complex analytic map from the tanegnt space of a point of a simply connected manifold to the manifold.