An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging
From MaRDI portal
Publication:3458222
DOI10.1088/0266-5611/31/11/115011zbMath1329.35351OpenAlexW1841853452MaRDI QIDQ3458222
Martin Storath, Andreas Weinmann, Kilian Hohm
Publication date: 18 December 2015
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0266-5611/31/11/115011
ADMMinverse problemdynamic programmingcomputed tomographyimage reconstructiondeconvolutionMumford-Shah functional
Related Items (14)
Constrained energy variation for change point detection ⋮ Mumford-Shah and Potts regularization for manifold-valued data ⋮ Mumford–Shah regularization in electrical impedance tomography with complete electrode model ⋮ Task adapted reconstruction for inverse problems ⋮ Mumford-Shah-TV functional with application in X-ray interior tomography ⋮ Image inpainting using non-convex low rank decomposition and multidirectional search ⋮ An image inpainting algorithm using exemplar matching and low-rank sparse prior ⋮ Shape-based image reconstruction using linearized deformations ⋮ An Algorithm for Second Order Mumford--Shah Models Based on a Taylor Jet Formulation ⋮ Non-smooth Variational Regularization for Processing Manifold-Valued Data ⋮ Iterative Potts minimization for the recovery of signals with discontinuities from indirect measurements: the multivariate case ⋮ Smoothing for signals with discontinuities using higher order Mumford-Shah models ⋮ Multi-channel Potts-based reconstruction for multi-spectral computed tomography ⋮ XCT image reconstruction by a modified superiorized iteration and theoretical analysis
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- A Mumford-Shah level-set approach for the inversion and segmentation of SPECT/CT data
- Iterative thresholding meets free-discontinuity problems
- A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
- On the regularization of the inverse conductivity problem with discontinuous conductivities
- Locally adaptive regression splines
- Local extremes, runs, strings and multiresolution. (With discussion)
- A first-order primal-dual algorithm for convex problems with applications to imaging
- Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data
- The equivalence of the taut string algorithm and BV-regularization
- Optimal approximations by piecewise smooth functions and associated variational problems
- Regularization of ill-posed Mumford–Shah models with perimeter penalization
- A Mumford–Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- A Semismooth Newton Method for $\mathrm{L}^1$ Data Fitting with Automatic Choice of Regularization Parameters and Noise Calibration
- Limited Data X-Ray Tomography Using Nonlinear Evolution Equations
- Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
- Monotone Operators and the Proximal Point Algorithm
- Finite-differences discretizations of the mumford-shah functional
- Enhanced Electrical Impedance Tomographyviathe Mumford–Shah Functional
- Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification
- Jump-Sparse and Sparse Recovery Using Potts Functionals
- Disparity and optical flow partitioning using extended Potts priors
- Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction
- Smoothers for Discontinuous Signals
- Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations
- Optimal Detection of Changepoints With a Linear Computational Cost
- Fast Partitioning of Vector-Valued Images
- Joint image reconstruction and segmentation using the Potts model
- Iterative Potts and Blake–Zisserman minimization for the recovery of functions with discontinuities from indirect measurements
- On the Complexity of Mumford–Shah-Type Regularization, Viewed as a Relaxed Sparsity Constraint
- Scale Space and PDE Methods in Computer Vision
This page was built for publication: An algorithmic framework for Mumford–Shah regularization of inverse problems in imaging
