Person

Martin Kurt Storath

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Related publications (17)

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We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signat ...

Elsevier2017

Fast Segmentation from Blurred Data in 3D Fluorescence Microscopy

Michaël Unser, Martin Kurt Storath

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of deali ...

2017

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We study jump-penalized estimators based on least absolute deviations which are often referred to as Potts estimators. They are estimators for a parsimonious piecewise constant representation of noisy data having a noise distribution which has heavier tail ...

Oxford University Press2017

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Martin Kurt Storath

Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and non-convex, they are ...

Springer2016

Transforms and Operators for Directional Bioimage Analysis: A Survey

Michaël Unser, Daniel Sage, Zsuzsanna Püspöki, Martin Kurt Storath

We give a methodology-oriented perspective on directional image analysis and rotation-invariant processing. We review the state of the art in the field and make connections with recent mathematical developments in functional analysis and wavelet theory. We ...

Springer International Publishing2016

The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this pap ...

Iop Publishing Ltd2015

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

Martin Kurt Storath

Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities descr ...

Royal Soc2015

Joint image reconstruction and segmentation using the Potts model

Michaël Unser, Martin Kurt Storath

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficie ...

Institute of Physics2015

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 Gamma-convergence of discrete L-1-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimi ...

Siam Publications2015

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

SIAM2016