Publications related to A Second-Order Extension Of Tv Regularization For Image Deblurring

Related publications (29)

Towards Trustworthy Deep Learning for Image Reconstruction

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

American Mathematical Society (AMS)2023

Regularization of polynomial networks for image recognition

Volkan Cevher, Grigorios Chrysos, Bohan Wang

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising ...

2023

Regularization of polynomial networks for image recognition

Volkan Cevher, Grigorios Chrysos, Bohan Wang

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising ...

Ieee Computer Soc2023

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Thomas Jean Debarre

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

EPFL2022

Stochastic derivative estimation for max-stable random fields

Erwan Fabrice Koch

We consider expected performances based on max-stable random fields and we are interested in their derivatives with respect to the spatial dependence parameters of those fields. Max-stable fields, such as the Brown-Resnick and Smith fields, are very popula ...

ELSEVIER2022

Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension

Robert Dalang

We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, ...

INST MATHEMATICAL STATISTICS-IMS2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

2020

On design strategies for binary dielectric metasurfaces based on the Fourier modal method

Kévin Müller

Binary dielectric metasurfaces are arrays of sub-wavelength structures that act as a thin layer of artificial material. They are generally lossless and relatively simple to fabricate since only a single structuring step is required. By carefully designing ...

EPFL2020

Adaptive Regularization For Three-Dimensional Optical Diffraction Tomography

Michaël Unser, Demetri Psaltis, Emmanuel Emilien Louis Soubies, Thanh-An Michel Pham, Ahmed Bassam Sayed Ayoub Mohamed Emam

Optical diffraction tomography (ODT) allows one to quantitatively measure the distribution of the refractive index of the sample. It relies on the resolution of an inverse scattering problem. Due to the limited range of views as well as optical aberrations ...

IEEE2020

Local Non-Rigid Structure-from-Motion from Locally Diffeomorphic Mappings

Pascal Fua, Mathieu Salzmann, Shaifali Parashar

We propose a new formulation to the non-rigid structure-from-motion problem that only requires the deforming surface to meaning that its differential structure is preserved. This is a much weaker assumption than the traditional ones of isometry or conforma ...

2020

A note on efficient computation of privileged directions in modifier adaptation

Dominique Bonvin, Timm Faulwasser, Alejandro Gabriel Marchetti, Martand Singhal

In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially pe ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Sparse wars: A survey and comparative study of spherical deconvolution algorithms for diffusion MRI

Jean-Philippe Thiran, Erick Jorge Canales Rodriguez, Gabriel Girard, David Paul Roger Romascano, Jonathan Rafael Patino Lopez, Alessandro Daducci, Muhamed Barakovic, Marco Pizzolato, Gaëtan Olivier D Rensonnet

Spherical deconvolution methods are widely used to estimate the brain's white-matter fiber orientations from diffusion MRI data. In this study, eight spherical deconvolution algorithms were implemented and evaluated. These included two model selection tech ...

2019

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

Steady Three-Dimensional Rotational Flows: An Approach Via Two Stream Functions And Nash-Moser Iteration

Boris Buffoni

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) x R-2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of ...

MATHEMATICAL SCIENCE PUBL2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy, Anastasiia Koloskova

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

2019

To positivity and beyond, where Higgs-Dilaton inflation has never gone before

Inar Timiryasov, Mario Herrero Valea, Anna Tokareva

We study the consequences of (beyond) positivity of scattering amplitudes in the effective field theory description of the Higgs-Dilaton inflationary model. By requiring the EFT to be compatible with a unitary, causal, local and Lorentz invariant UV comple ...

IOP PUBLISHING LTD2019

Fast and robust estimation of NODDI parameters using non-Gaussian noise models and spatial regularization

Jean-Philippe Thiran, Alessandro Daducci, Erick Jorge Canales Rodriguez

In this study, we developed a robust inversion algorithm to estimate the Neurite Orientation Dispersion and Density Imaging (NODDI) model. It is based on the Accelerated Microstructure Imaging via Convex Optimization (AMICO) framework. However, in contrast ...

2018

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

Michaël Unser, Julien René 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