Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Data‐driven methods for quantitative imaging

Guozhi Dong, Moritz Flaschel, Michael Hintermüller, Kostas Papafitsoros, Clemens Sirotenko and Karsten Tabelow
GAMM-Mitteilungen 48 (1) (2025)
https://doi.org/10.1002/gamm.202470014

Uncertainty Quantification for Scale-Space Blob Detection

Fabian Parzer, Clemens Kirisits and Otmar Scherzer
Journal of Mathematical Imaging and Vision 66 (4) 697 (2024)
https://doi.org/10.1007/s10851-024-01194-x

Variational Model with Nonstandard Growth Condition in Image Restoration and Contrast Enhancement

Ciro D’Apice, Peter I. Kogut, Rosanna Manzo and Antonino Parisi
Communications on Applied Mathematics and Computation (2024)
https://doi.org/10.1007/s42967-024-00382-1

Exact recovery of the support of piecewise constant images via total variation regularization

Yohann De Castro, Vincent Duval and Romain Petit
Inverse Problems 40 (10) 105012 (2024)
https://doi.org/10.1088/1361-6420/ad75b1

A Novel Density Based Approach for Topology Optimization of Stokes Flow

Johannes Haubner, Franziska Neumann and Michael Ulbrich
SIAM Journal on Scientific Computing 45 (2) A338 (2023)
https://doi.org/10.1137/21M143114X

A bilevel optimization problem with deep learning based on fractional total variation for image denoising

Anouar Ben-loghfyry and Abdelilah Hakim
Multimedia Tools and Applications 83 (10) 28595 (2023)
https://doi.org/10.1007/s11042-023-16583-4

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Juan Carlos De los Reyes and David Villacís
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging 909 (2023)
https://doi.org/10.1007/978-3-030-98661-2_66

ABPO-TVSCAD: alternating Bregman proximity operators approach based on TVSCAD regularization for bioluminescence tomography

Yi Chen, Mengfei Du, Weitong Li, et al.
Physics in Medicine & Biology 67 (21) 215013 (2022)
https://doi.org/10.1088/1361-6560/ac994c

Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization

Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg and Hongpeng Sun
Numerical Functional Analysis and Optimization 43 (8) 887 (2022)
https://doi.org/10.1080/01630563.2022.2069812

Optimality Conditions for Bilevel Imaging Learning Problems with Total Variation Regularization

Juan Carlos De los Reyes and David Villacís
SIAM Journal on Imaging Sciences 15 (4) 1646 (2022)
https://doi.org/10.1137/21M143412X

Image Denoising Via Spatially Adaptive Directional Total Generalized Variation

Elaheh Tavakkol, Yiqiu Dong and Seyed-Mohammad Hosseini
Iranian Journal of Science and Technology, Transactions A: Science 46 (4) 1283 (2022)
https://doi.org/10.1007/s40995-022-01342-1

Constrained deconvolution from wavefront sensing using the frozen flow hypothesis and complex wavelet regularization

Zhilei Ren, Jin Liu and Yonghui Liang
Applied Optics 61 (2) 410 (2022)
https://doi.org/10.1364/AO.444869

Research Note: Recovering sparse models in 3D potential‐field inversion without bound dependence or staircasing problems using a mixed Lp norm regularization

Jiajia Sun and Xiaolong Wei
Geophysical Prospecting 69 (4) 901 (2021)
https://doi.org/10.1111/1365-2478.13063

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Juan Carlos De los Reyes and David Villacís
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging 1 (2021)
https://doi.org/10.1007/978-3-030-03009-4_66-1

Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

Riccardo Cristoferi
Journal of Applied Analysis 27 (1) 13 (2021)
https://doi.org/10.1515/jaa-2020-2031

On Decomposition Models in Imaging Sciences and Multi-time Hamilton--Jacobi Partial Differential Equations

Jérôme Darbon and Tingwei Meng
SIAM Journal on Imaging Sciences 13 (2) 971 (2020)
https://doi.org/10.1137/19M1266332

Characterization of Spatially Graded Biomechanical Scaffolds

Nicholas R. Hugenberg, Li Dong, James A. Cooper, David T. Corr and Assad A. Oberai
Journal of Biomechanical Engineering 142 (7) (2020)
https://doi.org/10.1115/1.4045905

Tube-Based Taut String Algorithms for Total Variation Regularization

Artyom Makovetskii, Sergei Voronin, Vitaly Kober and Aleksei Voronin
Mathematics 8 (7) 1141 (2020)
https://doi.org/10.3390/math8071141

Image Restoration by Combined Order Regularization with Optimal Spatial Adaptation

Sanjay Viswanath, Manu Ghulyani, Simon De Beco, Maxime Dahan and Muthuvel Arigovindan
IEEE Transactions on Image Processing 1 (2020)
https://doi.org/10.1109/TIP.2020.2988146

An accelerated primal-dual iterative scheme for the L 2 -TV regularized model of linear inverse problems

Wenyi Tian and Xiaoming Yuan
Inverse Problems 35 (3) 035002 (2019)
https://doi.org/10.1088/1361-6420/aaf70a

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2

Michael Hintermüller and Kostas Papafitsoros
Handbook of Numerical Analysis, Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2 20 437 (2019)
https://doi.org/10.1016/bs.hna.2019.08.001

Convergence rates and structure of solutions of inverse problems with imperfect forward models

Martin Burger, Yury Korolev and Julian Rasch
Inverse Problems 35 (2) 024006 (2019)
https://doi.org/10.1088/1361-6420/aaf6f5

Analysis of Optimal Control Problems of Semilinear Elliptic Equations by BV-Functions

Eduardo Casas and Karl Kunisch
Set-Valued and Variational Analysis 27 (2) 355 (2019)
https://doi.org/10.1007/s11228-018-0482-7

Scale Space and Variational Methods in Computer Vision

Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb and Christiane Stollenwerk
Lecture Notes in Computer Science, Scale Space and Variational Methods in Computer Vision 11603 485 (2019)
https://doi.org/10.1007/978-3-030-22368-7_38

Analysis and automatic parameter selection of a variational model for mixed Gaussian and salt-and-pepper noise removal

Luca Calatroni and Kostas Papafitsoros
Inverse Problems 35 (11) 114001 (2019)
https://doi.org/10.1088/1361-6420/ab291a

An Anisotropic Inf-Convolution BV Type Model for Dynamic Reconstruction

Maïtine Bergounioux and E. Papoutsellis
SIAM Journal on Imaging Sciences 11 (1) 129 (2018)
https://doi.org/10.1137/16M1104937

An adaptive iteration reconstruction method for limited-angle CT image reconstruction

Chengxiang Wang, Li Zeng, Lingli Zhang, Yumeng Guo and Wei Yu
Journal of Inverse and Ill-posed Problems 26 (6) 771 (2018)
https://doi.org/10.1515/jiip-2017-0034

Convergence Analysis of Primal–Dual Based Methods for Total Variation Minimization with Finite Element Approximation

WenYi Tian and Xiaoming Yuan
Journal of Scientific Computing 76 (1) 243 (2018)
https://doi.org/10.1007/s10915-017-0623-4

Variational Decompression of Image Data From DjVu Encoded Files

Martin Holler and Kamil S. Kazimierski
IEEE Transactions on Image Processing 27 (1) 490 (2018)
https://doi.org/10.1109/TIP.2017.2760513

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models

J. C. De los Reyes, C.-B. Schönlieb and T. Valkonen
Journal of Mathematical Imaging and Vision 57 (1) 1 (2017)
https://doi.org/10.1007/s10851-016-0662-8

Geometric properties of solutions to the total variation denoising problem

Antonin Chambolle, Vincent Duval, Gabriel Peyré and Clarice Poon
Inverse Problems 33 (1) 015002 (2017)
https://doi.org/10.1088/0266-5611/33/1/015002

Total Variation Denoising in $l^1$ Anisotropy

Michał Łasica, Salvador Moll and Piotr B. Mucha
SIAM Journal on Imaging Sciences 10 (4) 1691 (2017)
https://doi.org/10.1137/16M1103610

Analytical aspects of spatially adapted total variation regularisation

Michael Hintermüller, Konstantinos Papafitsoros and Carlos N. Rautenberg
Journal of Mathematical Analysis and Applications 454 (2) 891 (2017)
https://doi.org/10.1016/j.jmaa.2017.05.025

A fractional-order derivative based variational framework for image denoising

Yunmei Chen and Fangfang Dong
Inverse Problems and Imaging 10 (1) 27 (2016)
https://doi.org/10.3934/ipi.2016.10.27

Infimal Convolution Regularisation Functionals of BV and $$\varvec{\mathrm {L}}^{\varvec{p}}$$ L p Spaces

Martin Burger, Konstantinos Papafitsoros, Evangelos Papoutsellis and Carola-Bibiane Schönlieb
Journal of Mathematical Imaging and Vision 55 (3) 343 (2016)
https://doi.org/10.1007/s10851-015-0624-6

Linearized primal-dual methods for linear inverse problems with total variation regularization and finite element discretization

Wenyi Tian and Xiaoming Yuan
Inverse Problems 32 (11) 115011 (2016)
https://doi.org/10.1088/0266-5611/32/11/115011

Scale Space and Variational Methods in Computer Vision

Eva-Maria Brinkmann, Martin Burger and Joana Grah
Lecture Notes in Computer Science, Scale Space and Variational Methods in Computer Vision 9087 191 (2015)
https://doi.org/10.1007/978-3-319-18461-6_16

X‐ray computed tomography using curvelet sparse regularization

Matthias Wieczorek, Jürgen Frikel, Jakob Vogel, Elena Eggl, Felix Kopp, Peter B. Noël, Franz Pfeiffer, Laurent Demaret and Tobias Lasser
Medical Physics 42 (4) 1555 (2015)
https://doi.org/10.1118/1.4914368

A study of the one dimensional total generalised variation regularisation problem

Konstantinos Papafitsoros and Kristian Bredies
Inverse Problems & Imaging 9 (2) 511 (2015)
https://doi.org/10.3934/ipi.2015.9.511

Split Bregmanized anisotropic total variation model for image deblurring

Huasong Chen, Chunyong Wang, Yang Song and Zhenhua Li
Journal of Visual Communication and Image Representation 31 282 (2015)
https://doi.org/10.1016/j.jvcir.2015.07.004

Analysis and Application of a Nonlocal Hessian

Jan Lellmann, Konstantinos Papafitsoros, Carola Schönlieb and Daniel Spector
SIAM Journal on Imaging Sciences 8 (4) 2161 (2015)
https://doi.org/10.1137/140993818

The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising

Tuomo Valkonen
SIAM Journal on Mathematical Analysis 47 (4) 2587 (2015)
https://doi.org/10.1137/140976248

Local and Nonlocal Regularization to Image Interpolation

Yi Zhan, Sheng Jie Li, Meng Li and Yang Tang
Mathematical Problems in Engineering 2014 (1) (2014)
https://doi.org/10.1155/2014/230348

Efficient Algorithms for Global Optimization Methods in Computer Vision

Kristian Bredies
Lecture Notes in Computer Science, Efficient Algorithms for Global Optimization Methods in Computer Vision 8293 44 (2014)
https://doi.org/10.1007/978-3-642-54774-4_3

Level Set and PDE Based Reconstruction Methods in Imaging

Martin Burger and Stanley Osher
Lecture Notes in Mathematics, Level Set and PDE Based Reconstruction Methods in Imaging 2090 1 (2013)
https://doi.org/10.1007/978-3-319-01712-9_1

Posterior Expectation of the Total Variation Model: Properties and Experiments

Cécile Louchet and Lionel Moisan
SIAM Journal on Imaging Sciences 6 (4) 2640 (2013)
https://doi.org/10.1137/120902276

On behavior of signs for the heat equation and a diffusion method for data separation

Noriaki Umeda, Takeshi Ohtsuka, Yoshikazu Giga and Mi-Ho Giga
Communications on Pure and Applied Analysis 12 (5) 2277 (2013)
https://doi.org/10.3934/cpaa.2013.12.2277

A full second order variational model for multiscale texture analysis

Maïtine Bergounioux and Loïc Piffet
Computational Optimization and Applications 54 (2) 215 (2013)
https://doi.org/10.1007/s10589-012-9484-9

Properties ofL1-TGV2: The one-dimensional case

Kristian Bredies, Karl Kunisch and Tuomo Valkonen
Journal of Mathematical Analysis and Applications 398 (1) 438 (2013)
https://doi.org/10.1016/j.jmaa.2012.08.053

Spatially dependent regularization parameter selection in total generalized variation models for image restoration

Kristian Bredies, Yiqiu Dong and Michael Hintermüller
International Journal of Computer Mathematics 90 (1) 109 (2013)
https://doi.org/10.1080/00207160.2012.700400

Image Denoising via Nonlinear Hybrid Diffusion

Xiaoping Ji, Dazhi Zhang, Zhichang Guo and Boying Wu
Mathematical Problems in Engineering 2013 1 (2013)
https://doi.org/10.1155/2013/890157

Local behavior of sparse analysis regularization: Applications to risk estimation

Samuel Vaiter, Charles-Alban Deledalle, Gabriel Peyré, Charles Dossal and Jalal Fadili
Applied and Computational Harmonic Analysis 35 (3) 433 (2013)
https://doi.org/10.1016/j.acha.2012.11.006

Near-Optimal Compressed Sensing Guarantees for Total Variation Minimization

Deanna Needell and Rachel Ward
IEEE Transactions on Image Processing 22 (10) 3941 (2013)
https://doi.org/10.1109/TIP.2013.2264681

New Regularization Models for Image Denoising with a Spatially Dependent Regularization Parameter

Tian-Hui Ma, Ting-Zhu Huang and Xi-Le Zhao
Abstract and Applied Analysis 2013 1 (2013)
https://doi.org/10.1155/2013/729151

Computer Vision, Imaging and Computer Graphics. Theory and Application

Kristian Bredies and Martin Holler
Communications in Computer and Information Science, Computer Vision, Imaging and Computer Graphics. Theory and Application 359 242 (2013)
https://doi.org/10.1007/978-3-642-38241-3_16

Robust Sparse Analysis Regularization

Samuel Vaiter, Gabriel Peyre, Charles Dossal and Jalal Fadili
IEEE Transactions on Information Theory 59 (4) 2001 (2013)
https://doi.org/10.1109/TIT.2012.2233859

An Upwind Finite-Difference Method for Total Variation–Based Image Smoothing

Antonin Chambolle, Stacey E. Levine and Bradley J. Lucier
SIAM Journal on Imaging Sciences 4 (1) 277 (2011)
https://doi.org/10.1137/090752754

A duality-based approach to elliptic control problems in non-reflexive Banach spaces

Christian Clason and Karl Kunisch
ESAIM: Control, Optimisation and Calculus of Variations 17 (1) 243 (2011)
https://doi.org/10.1051/cocv/2010003

Anisotropic total variation regularized $L^1$ approximation and denoising/deblurring of 2D bar codes

Rustum Choksi, Yves van Gennip and Adam Oberman
Inverse Problems & Imaging 5 (3) 591 (2011)
https://doi.org/10.3934/ipi.2011.5.591

ON THE GRADIENT FLOW OF A ONE-HOMOGENEOUS FUNCTIONAL

ARIELA BRIANI, ANTONIN CHAMBOLLE, MATTEO NOVAGA and GIANDOMENICO ORLANDI
Confluentes Mathematici 03 (04) 617 (2011)
https://doi.org/10.1142/S1793744211000461

Reaction–diffusion systems with -growth for image denoising

Zhichang Guo, Qiang Liu, Jiebao Sun and Boying Wu
Nonlinear Analysis: Real World Applications 12 (5) 2904 (2011)
https://doi.org/10.1016/j.nonrwa.2011.04.015

Elliptic optimal control problems with L 1-control cost and applications for the placement of control devices

Georg Stadler
Computational Optimization and Applications 44 (2) 159 (2009)
https://doi.org/10.1007/s10589-007-9150-9

A Higher Order Model for Image Restoration: The One-Dimensional Case

G. Dal Maso, I. Fonseca, G. Leoni and M. Morini
SIAM Journal on Mathematical Analysis 40 (6) 2351 (2009)
https://doi.org/10.1137/070697823

Denoising of Frame Coefficients Using $\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization

Sylvain Durand and Mila Nikolova
Multiscale Modeling & Simulation 6 (2) 547 (2007)
https://doi.org/10.1137/06065828X

Staircasing in semidiscrete stabilised inverse linear diffusion algorithms

M. Breuß and M. Welk
Journal of Computational and Applied Mathematics 206 (1) 520 (2007)
https://doi.org/10.1016/j.cam.2006.08.006

Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional

Marius Lysaker and Xue-Cheng Tai
International Journal of Computer Vision 66 (1) 5 (2006)
https://doi.org/10.1007/s11263-005-3219-7

Variable Exponent, Linear Growth Functionals in Image Restoration

Yunmei Chen, Stacey Levine and Murali Rao
SIAM Journal on Applied Mathematics 66 (4) 1383 (2006)
https://doi.org/10.1137/050624522