Alternating Direction Method of Multipliers for Linear Inverse Problems

DOI10.1137/15M1029308zbMath1342.65137arXiv1601.02773MaRDI QIDQ5741060

Weijie Wang, Xiliang Lu, Qi-nian Jin, Yu Ling Jiao

Publication date: 21 July 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02773

zbMATH Keywords

convergencealternating direction method of multiplierslinear inverse problemsBregman distanceregularization property

Mathematics Subject Classification ID

Convex programming (90C25) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

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Uses Software

• RecPF

Cites Work

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• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Nonlinear total variation based noise removal algorithms
• Image restoration: a wavelet frame based model for piecewise smooth functions and beyond
• Regularization methods in Banach spaces.
• Finite element approximation of the Navier-Stokes equations
• Regularization of ill-posed linear equations by the non-stationary augmented Lagrangian method
• A unified primal-dual algorithm framework based on Bregman iteration
• Regularization with differential operators. I: General theory
• On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Framelets: MRA-based constructions of wavelet frames
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Deconvolution: a wavelet frame approach
• On the global and linear convergence of the generalized alternating direction method of multipliers
• Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms
• Multiplier and gradient methods
• The multiplier method of Hestenes and Powell applied to convex programming
• Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals
• Inverse Problems
• On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
• Morozov’s Principle for the Augmented Lagrangian Method Applied to Linear Inverse Problems
• Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective
• A Strictly Contractive Peaceman--Rachford Splitting Method for Convex Programming
• Regularization of linear ill-posed problems by the augmented Lagrangian method and variational inequalities
• Iterative regularization with a general penalty term—theory and application to L ¹ and TV regularization
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
• Image restoration: Total variation, wavelet frames, and beyond
• Faster Convergence Rates of Relaxed Peaceman-Rachford and ADMM Under Regularity Assumptions
• A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces
• An Iterative Regularization Method for Total Variation-Based Image Restoration
• Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond
• Convex analysis and monotone operator theory in Hilbert spaces

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