112 citations · 235 across the 6 of their papers we have counts for
7 papers
Mumford-Shah and Potts Regularization for Manifold-Valued Data with Applications to DTI and Q-Ball Imaging
Andreas Weinmann, Laurent Demaret, Martin 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…
Total variation regularization for manifold-valued data
Andreas Weinmann, Laurent Demaret, Martin Storath
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals w…
Irregular Sampling of the Radon Transform of Bandlimited Functions
Thomas Wiese, Laurent Demaret
We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform. First, we prove that the Radon transform is a continuo…
Jump-sparse and sparse recovery using Potts functionals
Martin Storath, Andreas Weinmann, Laurent Demaret
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 resul…
Complexity -penalized M-Estimation: Consistency in More Dimensions
Laurent Demaret, Felix Friedrich, Volkmar Liebscher +1
We study the asymptotics in for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains - e.g. images…
Signal Analysis based on Complex Wavelet Signs
Martin Storath, Laurent Demaret, Peter Massopust
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 t…
The L1-Potts functional for robust jump-sparse reconstruction
Andreas Weinmann, Martin Storath, Laurent Demaret
We investigate the non-smooth and non-convex -Potts functional in discrete and continuous time. We show -convergence of discrete -Potts functionals towards their conti…