Publications related to Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

2017

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Existence of solutions to a non-variational singular elliptic system with unbounded weights

Linda Maria De Cave

In this paper we prove an existence result for the following singular elliptic system {z > 0 in Omega, z is an element of W-0(iota,p)(Omega) : -Delta(p)z = a(x)z(q-iota)u(theta) , u > 0 in Omega, u is an element of W-0(iota,p)(Omega) : -Delta(p)u = b(x)z(q ...

Wiley-V C H Verlag Gmbh2017

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Motion Interaction Field for Accident Detection in Traffic Surveillance Video

Kwang Moo Yi, Seungryong Kim

This paper presents a novel method for modeling of interaction among multiple moving objects to detect traffic accidents. The proposed method to model object interactions is motivated by the motion of water waves responding to moving objects on water surfa ...

2014

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

Ieee2012

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functiona ...

IEEE2012

A Dual Algorithm For L1-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

The importance of priors for l2 regularization and total variation methods in quantitative susceptibility mapping

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

Phase imaging has been demonstrated to offer a good contrast between and within brain tissues at 7T[1] with iron and myelin concentration being amongst the main modulators of the observed contrast due to their para- and dia-magnetic properties.Phase imagin ...

2012

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

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Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Stochastic partial differential equations driven by Lévy white noises

Existence of solutions to a non-variational singular elliptic system with unbounded weights

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Motion Interaction Field for Accident Detection in Traffic Surveillance Video

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Hessian-Based Regularization for 3-D Microscopy Image Restoration

A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

The importance of priors for l2 regularization and total variation methods in quantitative susceptibility mapping

Stochastic partial differential equations driven by Lévy white noises

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Motion Interaction Field for Accident Detection in Traffic Surveillance Video

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Hessian-Based Regularization for 3-D Microscopy Image Restoration

The importance of priors for l2 regularization and total variation methods in quantitative susceptibility mapping

A Dual Algorithm For L1-Regularized Reconstruction Of Vector Fields

Existence of solutions to a non-variational singular elliptic system with unbounded weights