An introduction to continuous optimization for imaging
type: Item
instance of: scholarly article
title: An introduction to continuous optimization for imaging
zbMATH Open document ID: 1343.65064
DOI: 10.1017/S096249291600009X
author: Antonin Chambolle
author: Thomas Pock
published in: Acta Numerica
publication date: 2016-07-08T00:00:00Z
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 6601880
zbMATH Keywords: continuous optimization
zbMATH Keywords: algorithm
zbMATH Keywords: non-smooth problem
zbMATH Keywords: denoising
zbMATH Keywords: deblurring
zbMATH Keywords: magnetic resonance imaging
zbMATH Keywords: multilabel image segmentation
zbMATH Keywords: optical flow estimation
zbMATH Keywords: stereo matching
MaRDI profile type: Publication
cites work: Tight convex relaxations for vector-valued labeling
cites work: The natural vectorial total variation which arises from geometric measure theory
cites work: Fast multiple-splitting algorithms for convex optimization
cites work: Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
cites work: Proximal Minimization Methods with Generalized Bregman Functions
cites work: Deblurring and Denoising of Images by Nonlocal Functionals
cites work: The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces
cites work: A Fast Parametric Maximum Flow Algorithm and Applications
cites work: A dual algorithm for the solution of nonlinear variational problems via finite element approximation
cites work: A generalized proximal point algorithm for certain non-convex minimization problems
cites work: Regularized Discrete Optimal Transport
cites work: Accelerated, Parallel, and Proximal Coordinate Descent
cites work: A Variable Metric Proximal Point Algorithm for Monotone Operators
cites work: A Review of Image Denoising Algorithms, with a New One
cites work: The solution by iteration of nonlinear functional equations in Banach spaces
cites work: Convergence theorems for sequences of nonlinear operators in Banach spaces
cites work: A Monotone+Skew Splitting Model for Composite Monotone Inclusions in Duality
cites work: Produits infinis de resolvantes
cites work: Q5665783
cites work: Fast dual minimization of the vectorial total variation norm and applications to color image processing
cites work: A Convex, Lower Semicontinuous Approximation of Euler's Elastica Energy
cites work: Convex relaxation of a class of vertex penalizing functionals
cites work: Minimization of non-smooth, non-convex functionals by iterative thresholding
cites work: Total Generalized Variation
cites work: Preconditioned Douglas-Rachford algorithms for TV- and TGV-regularized variational imaging problems
cites work: Preconditioned Douglas--Rachford Splitting Methods for Convex-concave Saddle-point Problems
cites work: Linear convergence of iterative soft-thresholding
cites work: Soap films and covering spaces
cites work: Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
cites work: On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems
cites work: Duality and Convex Programming
cites work: On the convergence of primal-dual hybrid gradient algorithms for total variation image restoration
cites work: Proximal alternating linearized minimization for nonconvex and nonsmooth problems
cites work: The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
cites work: A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
cites work: Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities
cites work: Global Solutions of Variational Models with Convex Regularization
cites work: Minimum cuts and related problems
cites work: Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
cites work: Error forgetting of Bregman iteration
cites work: Over-relaxation of the fast iterative shrinkage-thresholding algorithm with variable stepsize
cites work: A Variable Metric Extension of the Forward–Backward–Forward Algorithm for Monotone Operators
cites work: Nonlinear total variation based noise removal algorithms
cites work: A splitting algorithm for dual monotone inclusions involving cocoercive operators
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: A generalized forward-backward splitting
cites work: Parallel Proximal Algorithm for Image Restoration Using Hybrid Regularization
cites work: Closed-Form MMSE Estimation for Signal Denoising Under Sparse Representation Modeling Over a Unitary Dictionary
cites work: Accelerated and inexact forward-backward algorithms
cites work: A primal–dual hybrid gradient method for nonlinear operators with applications to MRI
cites work: Block-coordinate gradient descent method for linearly constrained nonsmooth separable optimization
cites work: Convergence of a block coordinate descent method for nondifferentiable minimization
cites work: Learning the Morphological Diversity
cites work: Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
cites work: Entropic Proximal Mappings with Applications to Nonlinear Programming
cites work: Convex relaxation of vectorial problems with coupled regularization
cites work: Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set.

An introduction to continuous optimization for imaging (cites work)
cites work: A direct variational approach to a problem arising in image reconstruction

An introduction to continuous optimization for imaging (cites work)
cites work: The Primal-Dual Hybrid Gradient Method for Semiconvex Splittings

An introduction to continuous optimization for imaging (cites work)
cites work: An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping

An introduction to continuous optimization for imaging (cites work)
cites work: Monotone (nonlinear) operators in Hilbert space

An introduction to continuous optimization for imaging (cites work)
cites work: Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space

An introduction to continuous optimization for imaging (cites work)
cites work: A minimization method for the sum of a convex function and a continuously differentiable function

An introduction to continuous optimization for imaging (cites work)
cites work: Deconvolving Images With Unknown Boundaries Using the Alternating Direction Method of Multipliers

An introduction to continuous optimization for imaging (cites work)
cites work: The calibration method for the Mumford-Shah functional and free-discontinuity problems

An introduction to continuous optimization for imaging (cites work)
cites work: Maximum flows and minimum cuts in the plane

An introduction to continuous optimization for imaging (cites work)
cites work: Maximal flow through a domain

An introduction to continuous optimization for imaging (cites work)
cites work: Removing multiplicative noise by Douglas-Rachford splitting methods

An introduction to continuous optimization for imaging (cites work)
cites work: Sparse Image and Signal Processing

An introduction to continuous optimization for imaging (cites work)
cites work: An Accelerated Linearized Alternating Direction Method of Multipliers

An introduction to continuous optimization for imaging (cites work)
cites work: Weak convergence of the sequence of successive approximations for nonexpansive mappings

An introduction to continuous optimization for imaging (cites work)
cites work: Adaptive restart for accelerated gradient schemes

An introduction to continuous optimization for imaging (cites work)
cites work: Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring

An introduction to continuous optimization for imaging (cites work)
cites work: iPiano: inertial proximal algorithm for nonconvex optimization

An introduction to continuous optimization for imaging (cites work)
cites work: iPiasco: inertial proximal algorithm for strongly convex optimization

An introduction to continuous optimization for imaging (cites work)
cites work: Regularizing flows for constrained matrix-valued images

An introduction to continuous optimization for imaging (cites work)
cites work: Universal gradient methods for convex optimization problems

An introduction to continuous optimization for imaging (cites work)
cites work: Gradient methods for minimizing composite functions

An introduction to continuous optimization for imaging (cites work)
cites work: Efficiency of coordinate descent methods on huge-scale optimization problems

An introduction to continuous optimization for imaging (cites work)
cites work: Smooth minimization of non-smooth functions

An introduction to continuous optimization for imaging (cites work)
cites work: Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems

An introduction to continuous optimization for imaging (cites work)
cites work: The cosparse analysis model and algorithms

An introduction to continuous optimization for imaging (cites work)
cites work: Optimal approximations by piecewise smooth functions and associated variational problems

An introduction to continuous optimization for imaging (cites work)
cites work: Convergence of a splitting inertial proximal method for monotone operators

An introduction to continuous optimization for imaging (cites work)
cites work: Proximité et dualité dans un espace hilbertien

An introduction to continuous optimization for imaging (cites work)
cites work: Remark on “algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”

An introduction to continuous optimization for imaging (cites work)
cites work: Q5565773

An introduction to continuous optimization for imaging (cites work)
cites work: Q3134551

An introduction to continuous optimization for imaging (cites work)
cites work: A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

An introduction to continuous optimization for imaging (cites work)
cites work: On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators

An introduction to continuous optimization for imaging (cites work)
cites work: Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming

An introduction to continuous optimization for imaging (cites work)
cites work: Sparse directional image representations using the discrete shearlet transform

An introduction to continuous optimization for imaging (cites work)
cites work: Collaborative total variation: a general framework for vectorial TV models

An introduction to continuous optimization for imaging (cites work)
cites work: Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors

An introduction to continuous optimization for imaging (cites work)
cites work: A simple algorithm for a class of nonsmooth convex-concave saddle-point problems

An introduction to continuous optimization for imaging (cites work)
cites work: Compressed sensing

An introduction to continuous optimization for imaging (cites work)
cites work: De-noising by soft-thresholding

An introduction to continuous optimization for imaging (cites work)
cites work: On the global and linear convergence of the generalized alternating direction method of multipliers

An introduction to continuous optimization for imaging (cites work)
cites work: Convergence Rate Analysis of Primal-Dual Splitting Schemes

An introduction to continuous optimization for imaging (cites work)
cites work: Local extremes, runs, strings and multiresolution. (With discussion)

An introduction to continuous optimization for imaging (cites work)
cites work: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

An introduction to continuous optimization for imaging (cites work)
cites work: Image restoration with discrete constrained total variation. II: Levelable functions, convex priors and non-convex cases

An introduction to continuous optimization for imaging (cites work)
cites work: Image restoration with discrete constrained total variation. I: Fast and exact optimization

An introduction to continuous optimization for imaging (cites work)
cites work: BM3D Frames and Variational Image Deblurring

An introduction to continuous optimization for imaging (cites work)
cites work: Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets

An introduction to continuous optimization for imaging (cites work)
cites work: Total cyclic variation and generalizations

An introduction to continuous optimization for imaging (cites work)
cites work: A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms

An introduction to continuous optimization for imaging (cites work)
cites work: Signal Recovery by Proximal Forward-Backward Splitting

An introduction to continuous optimization for imaging (cites work)
cites work: Variable metric forward–backward splitting with applications to monotone inclusions in duality

An introduction to continuous optimization for imaging (cites work)
cites work: Proximal Splitting Methods in Signal Processing

An introduction to continuous optimization for imaging (cites work)
cites work: Solving monotone inclusions via compositions of nonexpansive averaged operators

An introduction to continuous optimization for imaging (cites work)
cites work: A cortical based model of perceptual completion in the roto-translation space

An introduction to continuous optimization for imaging (cites work)
cites work: Variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function

An introduction to continuous optimization for imaging (cites work)
cites work: Insights Into Analysis Operator Learning: From Patch-Based Sparse Models to Higher Order MRFs

An introduction to continuous optimization for imaging (cites work)
cites work: Optimal Primal-Dual Methods for a Class of Saddle Point Problems

An introduction to continuous optimization for imaging (cites work)
cites work: Atomic Decomposition by Basis Pursuit

An introduction to continuous optimization for imaging (cites work)
cites work: A proximal-based deomposition method for compositions method for convex minimization problems

An introduction to continuous optimization for imaging (cites work)
cites work: Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions

An introduction to continuous optimization for imaging (cites work)
cites work: Q3056948

An introduction to continuous optimization for imaging (cites work)
cites work: $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

An introduction to continuous optimization for imaging (cites work)
cites work: Matching pursuits with time-frequency dictionaries

An introduction to continuous optimization for imaging (cites work)
cites work: Super-Resolution With Sparse Mixing Estimators

An introduction to continuous optimization for imaging (cites work)
cites work: An efficient algorithm for image segmentation, Markov random fields and related problems

An introduction to continuous optimization for imaging (cites work)
cites work: Multiplier and gradient methods

An introduction to continuous optimization for imaging (cites work)
cites work: On the Convergence of Primal-Dual Hybrid Gradient Algorithm

An introduction to continuous optimization for imaging (cites work)
cites work: On the convergence rate of Douglas-Rachford operator splitting method

An introduction to continuous optimization for imaging (cites work)
cites work: On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers

An introduction to continuous optimization for imaging (cites work)
cites work: Analysis Operator Learning and its Application to Image Reconstruction

An introduction to continuous optimization for imaging (cites work)
cites work: Splitting Algorithms for the Sum of Two Nonlinear Operators

An introduction to continuous optimization for imaging (cites work)
cites work: An Accelerated Randomized Proximal Coordinate Gradient Method and its Application to Regularized Empirical Risk Minimization

An introduction to continuous optimization for imaging (cites work)
cites work: Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints

An introduction to continuous optimization for imaging (cites work)
cites work: Optimality bounds for a variational relaxation of the image partitioning problem

An introduction to continuous optimization for imaging (cites work)
cites work: Continuous Multiclass Labeling Approaches and Algorithms

An introduction to continuous optimization for imaging (cites work)
cites work: Optimally Sparse Multidimensional Representation Using Shearlets

An introduction to continuous optimization for imaging (cites work)
cites work: New Proximal Point Algorithms for Convex Minimization

An introduction to continuous optimization for imaging (cites work)
cites work: Learning the parts of objects by non-negative matrix factorization

An introduction to continuous optimization for imaging (cites work)
cites work: On the Convergence of the Proximal Point Algorithm for Convex Minimization

An introduction to continuous optimization for imaging (cites work)
cites work: On the convergence of the block nonlinear Gauss-Seidel method under convex constraints

An introduction to continuous optimization for imaging (cites work)
cites work: Necessary and sufficient conditions for linear convergence of ℓ1-regularization

An introduction to continuous optimization for imaging (cites work)
cites work: Non-convex sparse regularisation

An introduction to continuous optimization for imaging (cites work)
cites work: Fast Alternating Direction Optimization Methods

An introduction to continuous optimization for imaging (cites work)
cites work: The Split Bregman Method for L1-Regularized Problems

An introduction to continuous optimization for imaging (cites work)
cites work: Convex programming in Hilbert space

An introduction to continuous optimization for imaging (cites work)
cites work: A nonlocal Bayesian image denoising algorithm

An introduction to continuous optimization for imaging (cites work)
cites work: Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms

An introduction to continuous optimization for imaging (cites work)
cites work: Compactly supported shearlets are optimally sparse

An introduction to continuous optimization for imaging (cites work)
cites work: A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

An introduction to continuous optimization for imaging (cites work)
cites work: Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models

An introduction to continuous optimization for imaging (cites work)
cites work: Active contours without edges

An introduction to continuous optimization for imaging (cites work)
cites work: Aspects of Total Variation RegularizedL1Function Approximation

An introduction to continuous optimization for imaging (cites work)
cites work: An Upwind Finite-Difference Method for Total Variation–Based Image Smoothing

An introduction to continuous optimization for imaging (cites work)
cites work: Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage

An introduction to continuous optimization for imaging (cites work)
cites work: A Convex Approach to Minimal Partitions

An introduction to continuous optimization for imaging (cites work)
cites work: A first-order primal-dual algorithm for convex problems with applications to imaging

An introduction to continuous optimization for imaging (cites work)
cites work: Image recovery via total variation minimization and related problems

An introduction to continuous optimization for imaging (cites work)
cites work: On the convergence of the iterates of the ``fast iterative shrinkage/thresholding algorithm''

An introduction to continuous optimization for imaging (cites work)
cites work: On total variation minimization and surface evolution using parametric maximum flows

An introduction to continuous optimization for imaging (cites work)
cites work: Image sharpening by flows based on triple well potentials

An introduction to continuous optimization for imaging (cites work)
cites work: An algorithm for mean curvature motion

An introduction to continuous optimization for imaging (cites work)
cites work: Finite-differences discretizations of the mumford-shah functional

An introduction to continuous optimization for imaging (cites work)
cites work: Robust principal component analysis?

An introduction to continuous optimization for imaging (cites work)
cites work: Fast Discrete Curvelet Transforms

An introduction to continuous optimization for imaging (cites work)
cites work: A Singular Value Thresholding Algorithm for Matrix Completion

An introduction to continuous optimization for imaging (cites work)
cites work: A Limited Memory Algorithm for Bound Constrained Optimization

An introduction to continuous optimization for imaging (cites work)
cites work: A Descent Numerical Method for Optimization Problems with Nondifferentiable Cost Functionals

An introduction to continuous optimization for imaging (cites work)
cites work: Inexact Bregman iteration with an application to Poisson data reconstruction

An introduction to continuous optimization for imaging (cites work)
cites work: Iterative Bregman Projections for Regularized Transportation Problems

An introduction to continuous optimization for imaging (cites work)
cites work: Lectures on modern convex optimization. Analysis, algorithms, and engineering applications

An introduction to continuous optimization for imaging (cites work)
cites work: Robust convex optimization

An introduction to continuous optimization for imaging (cites work)
cites work: NESTA: A Fast and Accurate First-Order Method for Sparse Recovery

An introduction to continuous optimization for imaging (cites work)
cites work: On the Convergence of Block Coordinate Descent Type Methods

An introduction to continuous optimization for imaging (cites work)
cites work: A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

An introduction to continuous optimization for imaging (cites work)
cites work: Mirror descent and nonlinear projected subgradient methods for convex optimization.

An introduction to continuous optimization for imaging (cites work)
cites work: On the Convergence of Alternating Minimization for Convex Programming with Applications to Iteratively Reweighted Least Squares and Decomposition Schemes

An introduction to continuous optimization for imaging (cites work)
cites work: Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality

An introduction to continuous optimization for imaging (cites work)
cites work: Convex analysis and monotone operator theory in Hilbert spaces

An introduction to continuous optimization for imaging (cites work)
cites work: Interior Gradient and Epsilon-Subgradient Descent Methods for Constrained Convex Minimization

An introduction to continuous optimization for imaging (cites work)
cites work: Stability of Over-Relaxations for the Forward-Backward Algorithm, Application to FISTA

An introduction to continuous optimization for imaging (cites work)
cites work: Algorithm 778: L-BFGS-B

An introduction to continuous optimization for imaging (cites work)
cites work: Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

An introduction to continuous optimization for imaging (cites work)
cites work: A unified primal-dual algorithm framework based on Bregman iteration

An introduction to continuous optimization for imaging (cites work)
cites work: Variational Analysis in Sobolev and BV Spaces

An introduction to continuous optimization for imaging (cites work)
cites work: Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization

An introduction to continuous optimization for imaging (cites work)
cites work: A Parallel Splitting Method for Coupled Monotone Inclusions

An introduction to continuous optimization for imaging (cites work)
cites work: Operator splittings, Bregman methods and frame shrinkage in image processing

An introduction to continuous optimization for imaging (cites work)
cites work: Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality

An introduction to continuous optimization for imaging (cites work)
cites work: The Elastic Ratio: Introducing Curvature Into Ratio-Based Image Segmentation

An introduction to continuous optimization for imaging (cites work)
cites work: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods

An introduction to continuous optimization for imaging (cites work)
cites work: Smooth Optimization with Approximate Gradient

An introduction to continuous optimization for imaging (cites work)
cites work: Minimization of functions having Lipschitz continuous first partial derivatives

An introduction to continuous optimization for imaging (cites work)
cites work: A variational framework for exemplar-based image inpainting

An introduction to continuous optimization for imaging (cites work)
cites work: Q4954179