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Martin Kurt Storath

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Related publications (17)

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The $ L ^{ 1 } $ -Potts Functional for Robust Jump-Sparse Reconstruction

Martin Kurt Storath

We investigate the nonsmooth and nonconvex

L ^{ 1 }

-Potts functional in discrete and continuous time. We show Γ-convergence of discrete

L ^{ 1 }

-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corr ...

SIAM2015

Disparity and Optical Flow Partitioning Using Extended Potts Priors

Martin Kurt Storath

This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow par ...

IMA2015

Total Variation Regularization of Shape Signals

Martin Kurt Storath

This paper introduces the concept of shape signals, i.e., series of shapes which have a natural temporal or spatial ordering, as well as a variational formulation for the regularization of these signals. The proposed formulation can be seen as the shape-va ...

IEEE2015

Fast Partitioning of Vector-Valued Images

Martin Kurt Storath

We propose a fast splitting approach to the classical variational formulation of the image partitioning problem, which is frequently referred to as the Potts or piecewise constant Mumford-Shah model. For vector-valued images, our approach is significantly ...

Siam Publications2014

Total Variation Regularization for Manifold-Valued Data

Martin Kurt Storath

We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...

Siam Publications2014

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...

Ieee-Inst Electrical Electronics Engineers Inc2014

We present a method for the unsupervised segmentation of textured images using Potts functionals, which are a piecewise-constant variant of the Mumford and Shah functionals. We propose a minimization strategy based on the alternating direction method of mu ...

IEEE2014

The $ L ^{ 1 } $ -Potts Functional for Robust Jump-Sparse Reconstruction

Martin Kurt Storath

We investigate the nonsmooth and nonconvex

L ^{ 1 }

-Potts functional in discrete and continuous time. We show Γ-convergence of discrete

L ^{ 1 }

-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corr ...

SIAM2015