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A Second-Order Extension of TV Regularization for Image Deblurring
Related publications (32)
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 ...
Providence2023Learning 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 INC2022Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution
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 ...
EPFL2022Polarity Of Almost All Points For Systems Of Nonlinear Stochastic Heat Equations In The Critical Dimension
We study vector-valued solutions u(t, x) is an element of R-d to systems of nonlinear stochastic heat equations with multiplicative noise, partial derivative/partial derivative t u(t, x) = partial derivative(2)/partial derivative x(2) u(t, x) + sigma (u(t, ...
INST MATHEMATICAL STATISTICS-IMS2021A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation
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 ...
2020On design strategies for binary dielectric metasurfaces based on the Fourier modal method
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 ...
EPFL2020Sparse 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, Marco Pizzolato, Jonathan Rafael Patino Lopez, Alessandro Daducci, Muhamed Barakovic, 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 ...
2019Sparse Gradient Optimization and its Applications in Image Processing
Nikolaos Arvanitopoulos Darginis
Millions of digital images are captured by imaging devices on a daily basis. The way imaging devices operate follows an integral process from which the information of the original scene needs to be estimated. The estimation is done by inverting the integra ...
EPFL2017Sparsity-Based Data Reconstruction Models for Biomedical Imaging
We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...
EPFL2016