Publications related to Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Non-local Functionals Related to the Total Variation and Connections with Image Processing

Hoài-Minh Nguyên

We present new results concerning the approximation of the total variation,

\int_{\Omega} |\nabla u|

, of a function

u

by non-local, non-convex functionals of the form $$ \Lambda_\delta u = \int_{\Omega} \int_{\Omega} \frac{\delta \varphi \big( |u(x) - ...

2018

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Martin Kurt 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 denoising and segmentation. Being both non-smooth and non-convex, they are ...

Springer2016

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

Shapes from pixels

Martin Vetterli, Arash Amini, Loïc Arnaud Baboulaz, Mitra Fatemi

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies ...

Institute of Electrical and Electronics Engineers2016

Numerical homogenization methods for parabolic monotone problems

Assyr Abdulle

In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. ...

2016

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Alfio Quarteroni, Paolo Pacciarini

We propose and analyse a new discontinuous reduced basis element method for the approximation of parametrized elliptic PDEs in partitioned domains. The method is built upon an offline stage (parameter independent) and an online (parameter dependent) one. I ...

Edp Sciences S A2016

The L-1-Potts Functional For Robust Jump-Sparse Reconstruction

Martin Kurt Storath

We investigate the nonsmooth and nonconvex L-1-Potts functional in discrete and continuous time. We show Gamma-convergence of discrete L-1-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimi ...

Siam Publications2015

An Algorithmic Framework for Mumford-Shah Regularization of Inverse Problems in Imaging

Martin Kurt Storath

The Mumford-Shah model is a very powerful variational approach for edge preserving regularization of image reconstruction processes. However, it is algorithmically challenging because one has to deal with a non-smooth and non-convex functional. In this pap ...

Iop Publishing Ltd2015

Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements

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A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Non-local Functionals Related to the Total Variation and Connections with Image Processing

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Shapes from pixels

Numerical homogenization methods for parabolic monotone problems

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

The L-1-Potts Functional For Robust Jump-Sparse Reconstruction

An Algorithmic Framework for Mumford-Shah Regularization of Inverse Problems in Imaging

Numerical homogenization methods for parabolic monotone problems

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Mumford-Shah and Potts Regularization for Manifold-Valued Data

Shapes from pixels

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Non-local Functionals Related to the Total Variation and Connections with Image Processing

A Discontinuous Galerkin Reduced Basis Element Method For Elliptic Problems

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

An Algorithmic Framework for Mumford-Shah Regularization of Inverse Problems in Imaging

The L-1-Potts Functional For Robust Jump-Sparse Reconstruction