A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

By Antonin Chambolle, Thomas Pock. 2011

2,706 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

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Citations in the corpus

Distributed Fixed Point Methods with Compressed Iterates (2019, methodology): “It is a generalization of Gradient Descent, Proximal Gradient Descent, and Douglas Rachford, ADMM and Chambolle-Pock algorithms [10] and it takes the form of fixed point iterations x = TVC(x).”
Optimal Algorithms for Non-Smooth Distributed Optimization in Networks (2018, methodology): “We solve it by applying Algorithm 1 in Chambolle-Pock [21] (we could alternatively apply composite Mirror-Prox [22]), which is both simple and well tailored to our problem: (a) it is an accelerated method for saddle-point problems, (b) it allows for composite problems with a sum of non-smooth and sm”
Stochastic Variance Reduction Methods for Saddle-Point Problems (2016, positive): “The algorithm from [20], which only applies to bilinear functions K , and which we extend from separable M to our more general set-up in Appendix B.”
Deep Unfolding Network for Image Super-Resolution (2020, methodology): “, half-quadratic splitting [2], alternating direction method of multipliers [6] and primal-dual [1, 9]) have been proposed to solve different image restoration tasks, such as image denoising [11, 32], image deblurring [29, 49], image compressive sensing [61, 63], and image demosaicking [28].”
Segmentation-Free Dynamic Scene Deblurring (2014, methodology): “(11) where n ≥ 0 indicates the iteration number, vector r denotes the dual variable of e and the positive update steps σ and τ control the convergence rate [2].”
A Primer on Monotone Operator Methods (2015, positive): “which we call the Chambolle-Pock method [28].”
FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging (2020, methodology): “First-order iterative proximal gradient methods, such as the Iterative Shrinkage/Thresholding Algorithm (ISTA) [3]–[5], Alternating Direction Method of Multipliers (ADMM) [6] and Primal-Dual Hybrid Gradient (PDHG) algorithm [7] are prevailing approaches to solve such problems with non-smooth regular”
Image Guided Depth Upsampling Using Anisotropic Total Generalized Variation (2013, methodology): “We formulate the upsampling as a convex optimization problem [2] [6].”
Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms (2013, methodology): “Reference [43] analyzes an exact method therein and establishes its convergence rates.”
Optimal Convergence Rates for Convex Distributed Optimization in Networks (2019, positive): “…and both strongly convex and smooth), the convergence rates of the Chambolle-Pock algorithm are weaker in such settings, and lead to convergence rates with respect to the distance to the optimum in squared norm (cid:107) θ t − θ ∗ (cid:107) 2 (see Chambolle and Pock, 2011, Theorems 2 and 3).”
A Field Guide to Forward-Backward Splitting with a FASTA Implementation (2014, methodology): “In many common domains, more complex splitting methods involving Lagrange multipliers (such as ADMM [50, 51] and its variants [52, 53]) are more commonly used.”
REMODE: Probabilistic, monocular dense reconstruction in real time (2014, methodology): “The solution to the minimization problem (6) is computed iteratively based on the work in [20].”
On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, neutral): “The authors would like to thank Antonin Chambolle for sending them [16] and for constructive comments, Frederik Simons for providing them with the list of source-receiver positions used in the synthetic example of section 7 and the two anonymous referees for their valuable remarks.”
An Inertial Forward-Backward Algorithm for Monotone Inclusions (2014, methodology): “αk = 0) algorithm [10] with the performance of its variants using either inertial forces using αk = 1/2 or overrelaxation (see (28)) using ρk = 1.”
A Convex Formulation for Hyperspectral Image Superresolution via Subspace-Based Regularization (2014, background): “Different approaches can be followed to factorize matrix Z , and two of them will be brieﬂy mentioned here.”