Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case
type: Item
instance of: scholarly article
title: Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case
zbMATH Open document ID: 1468.94019
author: Lukas Kiefer
author: Martin Storath
author: Andreas Weinmann
published in: Foundations of Computational Mathematics
publication date: 2021-07-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1812.00862
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 7371330
zbMATH Keywords: piecewise constant Mumford-Shah model
zbMATH Keywords: Potts model
zbMATH Keywords: majorization-minimization methods
zbMATH Keywords: image segmentation
zbMATH Keywords: joint reconstruction and segmentation
zbMATH Keywords: ill-posed inverse problems
zbMATH Keywords: Radon transform
zbMATH Keywords: deconvolution
describes a project that uses: AIR tools
describes a project that uses: MAXFLOW
describes a project that uses: pottslab
describes a project that uses: condat_tv
MaRDI profile type: Publication
OpenAlex ID: W3039927614
arXiv ID: 1812.00862
cites work: Q4954179
cites work: Approximation of functional depending on jumps by elliptic functional via t-convergence
cites work: Linearly constrained nonsmooth and nonconvex minimization
cites work: Global minimization for continuous multiphase partitioning problems using a dual approach
cites work: Computer Vision - ECCV 2004
cites work: Q3690580
cites work: Iterative thresholding for sparse approximations
cites work: Iterative hard thresholding for compressed sensing
cites work: Q4787357
cites work: Jump estimation in inverse regression
cites work: Consistencies and rates of convergence of jump-penalized least squares estimators
cites work: Completely convex formulation of the Chan-Vese image segmentation model
cites work: Enhancing sparsity by reweighted \(\ell _{1}\) minimization
cites work: Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
cites work: Finite-differences discretizations of the mumford-shah functional
cites work: A Convex Approach to Minimal Partitions
cites work: A first-order primal-dual algorithm for convex problems with applications to imaging
cites work: Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models
cites work: Active contours without edges
cites work: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
cites work: Q3973627
cites work: Q4895893
cites work: Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data
cites work: Iterative thresholding meets free-discontinuity problems
cites work: Multiscale Change Point Inference
cites work: Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
cites work: Tight convex relaxations for vector-valued labeling
cites work: Q5691133
cites work: AIR tools -- a MATLAB package of algebraic iterative reconstruction methods
cites work: An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging
cites work: Regularizing properties of the Mumford–Shah functional for imaging applications
cites work: Optimal Detection of Changepoints With a Linear Computational Cost
cites work: A Mumford–Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography
cites work: Regularization properties of Mumford-Shah-type functionals with perimeter and norm constraints for linear ill-posed problems
cites work: A Mumford-Shah level-set approach for the inversion and segmentation of SPECT/CT data
cites work: Iteration-complexity of first-order penalty methods for convex programming
cites work: An Iteration Formula for Fredholm Integral Equations of the First Kind
cites work: Continuous Multiclass Labeling Approaches and Algorithms
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators
cites work: Generalized methods and solvers for noise removal from piecewise constant signals. I: Background theory
cites work: Generalized methods and solvers for noise removal from piecewise constant signals. II: New methods
cites work: Iterative hard thresholding methods for \(l_0\) regularized convex cone programming
cites work: Sparse Approximation via Penalty Decomposition Methods
cites work: Optimal approximations by piecewise smooth functions and associated variational problems
cites work: Q3754464
cites work: Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization
cites work: Stable image reconstruction using total variation minimization

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cites work: Nonlinear total variation based noise removal algorithms

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cites work: Q3857636

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cites work: Smoothing for signals with discontinuities using higher order Mumford-Shah models

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cites work: Fast Partitioning of Vector-Valued Images

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cites work: Jump-Sparse and Sparse Recovery Using Potts Functionals

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cites work: Joint image reconstruction and segmentation using the Potts model

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cites work: $\ell _0$ Minimization for wavelet frame based image restoration

Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case (DOI)
DOI: 10.1007/S10208-020-09466-9

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