Publications related to A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

Mumford-Shah and Potts Regularization for Manifold-Valued Data

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

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Michaël Unser, Demetri Psaltis, Cédric René Jean Vonesch, Ulugbek Kamilov

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear coun ...

2016

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Michaël Unser, Nikolaos Stergiopoulos, Emrah Bostan, Orestis Vardoulis, Stamatios Lefkimmiatis

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

Ieee-Inst Electrical Electronics Engineers Inc2015

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Rolf Gruetter, Yves Wiaux, José Pedro Rebelo Ferreira Marques, Diana Khabipova

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l ...

Elsevier2015

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

Maria Colombo

In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow fo ...

2015

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Joachim Krieger

For the radial energy-supercritical nonlinear wave equation

\Box u = -u_{tt} + \triangle u = \pm u^7

on

\R^{3+1}

, we prove the existence of a class of global in forward time

C^\infty

-smooth solutions with infinite critical Sobolev norm $\dot{H}^{\f ...

Springer Verlag2014

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Michaël Unser, Stamatios Lefkimmiatis

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account t ...

Springer2013

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these req ...

IEEE2012

A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

Graph Chatbot

Chat with Graph Search

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

Variational Decomposition of Vector Fields in the Presence of Noise

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

Variational Decomposition of Vector Fields in the Presence of Noise

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems