Otmar Scherzer
Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction.
Fri, 08/19/2011 - 15:01 — SomNambulAuthors: Otmar Scherzer, Maarten V. de Hoop, Lingyun Qiu
Subjects: Functional Analysis
AbstractWe consider a class of inverse problems defined by a nonlinear map from
parameter or model functions to the data. We assume that solutions exist. The
space of model functions is a Banach space which is smooth and uniformly
convex; however, the data space can be an arbitrary Banach space. We study
sequences of parameter functions generated by a nonlinear Landweber iteration
and conditions under which these strongly converge, locally, to the solutions
within an appropriate distance.Photoacoustic Imaging Taking into Account Attenuation.
Thu, 09/23/2010 - 15:02 — SomNambulAuthors: Otmar Scherzer, Richard Kowar
Subjects: Analysis of PDEs
AbstractFirst, we review existing attenuation models and discuss their causality
properties, which we believe to be essential for algorithms for inversion with
attenuated data. Then, we survey causality properties of common attenuation
models. We also derive integro-differential equations which the attenuated
waves are satisfying. In addition we discuss the ill--conditionness of the
inverse problem for calculating the unattenuated wave from the attenuated one.A Derivative-Free Approach to Total Variation Regularization.
Mon, 11/09/2009 - 16:01 — SomNambulAuthors: Carsten Pontow, Otmar Scherzer
Subjects: Optimization and Control
AbstractThe goal of this paper is to present a novel approach for total variation
regularization and Sobolev minimization, which are prominent tools for
variational imaging. Thereby we use derivative free characterizations of the
total variation semi-norm and Sobolev semi-norms of functions recently derived
by Bourgain, Br\'ezis, Mironescu and D\'avila. Their analysis is to approximate
the semi-norms of a function by singular integral operators.
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