A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science

By Ernie Esser, Xiaoqun Zhang, Tony F. Chan. SIAM Journal of Imaging Sciences, 2010

739 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c474c1ee1f1fafa6f25f700089e9ca6ebbfcbd10

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Citations in the corpus

A New Primal–Dual Algorithm for Minimizing the Sum of Three Functions with a Linear Operator (2016, methodology): “, [32, 18,4]), while the primal-dual algorithm with g missing (Primal-Dual FixedPoint algorithm based on the Proximity Operator (PDFP(2)O) or Proximal Alternating Predictor-Corrector (PAPC)) is proposed in [27,7,17].”
An introduction to continuous optimization for imaging (2016, background): “More precisely, the algorithm we describe here would correspond to ‘PDHGMu’ and ‘PDHGMp’ in Esser et al. (2010), while ‘PDHG’ correspond to a plain Arrow–Hurwicz alternating scheme such as in Zhu and Chan (2008).”
A Primer on Monotone Operator Methods (2015, neutral): “This setup has been studied in several contexts such as image processing [23,48,133].”
A Primal–Dual Splitting Method for Convex Optimization Involving Lipschitzian, Proximable and Linear Composite Terms (2012, background): “2 exactly revert to the primal–dual algorithms of Chambolle and Pock [14], which have been proposed in other forms in [15, 16].”
A Three-Operator Splitting Scheme and its Optimization Applications (2015, background): “A large variety of recent algorithms [12,26,37] and their generalizations and enhancements [4,7,6,8,16,17, 18,20,28,39] are (skillful) applications of one of the following three operator-splitting schemes: (i) forwardbackward-forward splitting (FBFS) [38], (ii) forward-backward splitting (FBS) [36],”
Proximal Algorithms (2013, methodology): “In the image processing literature, it is known as the split inexact Uzawa method [80, 205, 204, 104].”
Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators (2015, background): “Particular cases of such fixed metric primal-algorithm can be found in [12, 15, 30, 34, 35].”
Convergence results of two-step inertial proximal point algorithm (2022, methodology): “The primal-dual hybrid gradient (PDHG) method (see, for example, [18,29]) is one of the popular methods for solving problem (58) and it is a preconditioned proximal point algorithm with λ = 1 for the saddle subdifferential operator of φ given in (53) (see, [19,34]).”
On the Convergence of Alternating Minimization for Convex Programming with Applications to Iteratively Reweighted Least Squares and Decomposition Schemes (2015, background): “Several approaches have been devised to solve the problem under different types of assumptions, see for example [13, 9, 27].”
Self Equivalence of the Alternating Direction Method of Multipliers (2014, background): “Paper [4] proposed a primal-dual algorithm for (20) and obtained the connection between ADM and that primal-dual algorithm [10]: When B = I, ADM is equivalent to the primal-dual algorithm in [4]; When B 6= I, the primal-dual algorithm is a preconditioned ADM as an additional proximal term δ/2‖y − y ”
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding (2013, methodology): “[63] for a detailed discussion of various first-order methods and the relationships between them, and Parikh and Boyd [64] for a survey of proximal algorithms in particular.”
Image Guided Depth Upsampling Using Anisotropic Total Generalized Variation (2013, methodology): “We formulate the upsampling as a convex optimization problem [2] [6].”
Image super-resolution: The techniques, applications, and future (2016, methodology): “The Bregman iterative regularization method, the Douglas-Rachford algorithm, and ADMM have been shown to be equivalent under the assumption of linear constraints [136,137].”