Workshop on Bioimaging II / PDEs, Mon, 19 Nov, 2007
Speaker: Frank Lenzen
Abstract
One way to motivate evolutionary partial differential equations is
to use semigroup theory on a variational formulation.
Based on a regularization functional iterative minimization with
regularization parameter $\tau$ is considered.
The PDE then is (formally) obtained as the asymptotic limit for $\tau\to 0$.
In our talk we are concerned with non-convex functionals on spaces of
vector-valued functions, where the numerical calculation of generalized minimizers is an open question.
We overcome this problem by applying semigroup theory and determining a gradient flow, ending up with a PDE, which in the case of scalar data becomes the well-known Mean Curvature Equation.
Additionally we present examples of applications, for which our PDE method is well suited for, e.g. denoising of vector-valued data, removing sampling point errors or compression artifacts and filtering upsampled data.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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