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First-order primal-dual algorithm for image restoration corrupted by mixed Poisson-Gaussian noise

SIGNAL PROCESSING-IMAGE COMMUNICATION 2023年第1期117卷

作者： Chen, Miao Wen, Meng Tang, Yuchao Nanchang Univ Dept Math Nanchang 330031 Peoples R China Xian Polytech Univ Sch Sci Xian 710048 Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China

The total variation infimal convolution (TV-IC) model combining Kullback-Leibler and ��2-norm data fidelit y term works wel l for the inverse problem of mixed Poisson-Gaussian noise. Most existing algorithms for solving the TV-IC model rely on the Newton method to solve a nonlinear optimization subproblem, which inevitably increases the computation burden. In this study, we apply the first-order primal-dual Chambolle- Pock algorithm to solve the TV-IC model . In particular, we present an effective algorithm to solve the subproblem of the joint proximal operator with the Kullback-Leibler divergence and ��2-norm, which is based on the bilinear constraint alternating direction multiplier method. Numerical experiment results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for mixed Poisson-Gaussian denoising and deblurring problems.

关键词： Mixed Poisson-Gaussian noise primal-dual algorithm Kullback-Leibler divergence Total variation

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Non-convex primal-dual algorithm for image reconstruction in spectral CT

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COMPUTERIZED MEDICAL IMAGING AND GRAPHICS 2021年 87卷 101821-101821页

作者： Chen, Buxin Zhang, Zheng Xia, Dan Sidky, Emil Y. Pan, Xiaochuan Univ Chicago Dept Radiol 5841 South Maryland AveMC2026 Chicago IL 60637 USA Univ Chicago Dept Radiat & Cellular Oncol Chicago IL 60637 USA

The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization program, and develop a non-convex primal-dual (NCPD) algorithm to solve the program. We devise multiple convergence conditions and perform verification studies numerically to demonstrate that the NCPD algorithm can solve the non-convex optimization program and under appropriate data condition, can invert the non-linear data model. Using the NCPD algorithm, we then reconstruct monochromatic images from simulated and real data of numerical and physical phantoms acquired with a standard, full-scan dual-energy configuration. The result of the reconstruction studies shows that the NCPD algorithm can correct accurately for the non-linear beam-hardening effect. Furthermore, we apply the NCPD algorithm to simulated and real data of the numerical and physical phantoms collected with non-standard, short-scan dual-energy configurations, and obtain monochromatic images comparable to those of the standard, full-scan study, thus revealing the potential of the NCPD algorithm for enabling non-standard scanning configurations in spectral CT, where the existing indirect methods are limited.

关键词： Spectral CT Photon-counting CT Image reconstruction Non-convex optimization primal-dual algorithm

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A stochastic primal-dual algorithm for composite constrained optimization

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NEUROCOMPUTING 2024年 604卷

作者： Su, Enbing Hu, Zhihuan Xie, Wei Li, Li Zhang, Weidong Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Tongji Univ Coll Elect & Informat Engn Shanghai 200240 Peoples R China Hainan Univ Sch Informat & Commun Engn Haikou 570228 Peoples R China

This paper studies the decentralized stochastic optimization problem over an undirected network, where each agent owns its local private functions made up of two non-smooth functions and an expectation-valued function. A decentralized stochastic primal-dual algorithm is proposed, by combining the variance-reduced method and the stochastic approximation method. The local gradients are estimated by using the mean of a variable number of sample gradients and the stochastic error decreases with the number of samples in the stochastic approximation process. The highlight of this paper is the extension of the primal-dual algorithm to the stochastic optimization problems. The effectiveness of the proposed algorithm and the correctness of the theory are verified by numerical experiments.

关键词： Stochastic approximation method Decentralized optimization primal-dual algorithm Variance reduction

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A primal-dual SGD algorithm for Distributed Nonconvex Optimization

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IEEE/CAA Journal of Automatica Sinica 2022年第5期9卷 812-833页

作者： Xinlei Yi Shengjun Zhang Tao Yang Tianyou Chai Karl Henrik Johansson Division of Decision and Control Systems School of Electrical Engineering and Computer ScienceKTH Royal Institute of Technologyand also affiliated with the Digital FuturesStockholm 10044Sweden Department of Electrical Engineering University of North TexasDentonTX 76203 USA IEEE State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110819China

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is *** problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated *** propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost *** show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of *** also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global *** demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

关键词： Distributed nonconvex optimization linear speedup Polyak-Lojasiewicz(P-L)condition primal-dual algorithm stochastic gradient descent

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A primal-dual approximation algorithm for the Asymmetric Prize-Collecting TSP

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2013年第2期25卷 265-278页

作者： Viet Hung Nguyen Univ Paris 06 LIP6 Paris France

We present a primal-dual aOElog(n)aOE parts per thousand-approximation algorithm for the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. The previous algorithm for the problem (V.H. Nguyen and T.T Nguyen in Int. J. Math. Oper. Res. 4(3):294-301, 2012) which is not combinatorial, is based on the Held-Karp relaxation and heuristic methods such as the Frieze et al.'s heuristic (Frieze et al. in Networks 12:23-39, 1982) or the recent Asadpour et al.'s heuristic for the ATSP (Asadpour et al. in 21st ACM-SIAM symposium on discrete algorithms, 2010). Depending on which of the two heuristics is used, it gives respectively 1+aOElog(n)aOE parts per thousand and as an approximation ratio. Our algorithm achieves an approximation ratio of aOElog(n)aOE parts per thousand which is weaker than but represents the first combinatorial approximation algorithm for the Asymmetric Prize-Collecting TSP.

关键词： Prize collecting Traveling Salesman Approximation algorithm primal-dual algorithm

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primal-dual approximation algorithm for the two-level facility location problem via a dual quasi-greedy approach

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THEORETICAL COMPUTER SCIENCE 2015年第C期562卷 213-226页

作者： Wu, Chenchen Du, Donglei Xu, Dachuan Tianjin Univ Technol Coll Sci Tianjin 300384 Peoples R China Univ New Brunswick Fac Business Adm Fredericton NB E3B 5A3 Canada Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China

The main contribution of this work is to propose a primal-dual combinatorial 3(1 + epsilon)-approximation algorithm for the two-level facility location problem (2-LFLP) by exploring the approximation oracle concept. This result improves the previous primal-dual 6-approximation algorithm for the multilevel facility location problem, and also matches the previous primal-dual approximation ratio for the single-level facility location problem. One of the major merits of primal-dual type algorithms is their easy adaption to other variants of the facility location problems. As a demonstration, our primal-dual approximation algorithm can be easily adapted to several variants of the 2-LFLP, including models with stochastic scenario, dynamically arrived demands, and linear facility cost. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Facility location problem Approximation algorithm primal-dual algorithm

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A Randomised primal-dual algorithm for Distributed Radio-Interferometric Imaging

A Randomised Primal-Dual Algorithm for Distributed Radio-Int...

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European Signal Processing Conference

作者： Alexandru Onose Rafael E. Carrillo Jason D. McEwen Yves Wiaux Institute of Sensors Signals and Systems Heriot-Watt University Signal Processing Laboratory (LTS5) Ecole Polytechnique Federale de Lausanne Mullard Space Science Laboratory University College London

ISBN: (纸本)9781509018918

Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets is of prime importance. Motivated by this, we investigate herein a convex optimisation algorithmic structure, based on primal-dual forward-backward iterations, for solving the radio interferometric imaging problem. It can encompass any convex prior of interest. It allows for the distributed processing of the measured data and introduces further flexibility by employing a probabilistic approach for the selection of the data blocks used at a given iteration. We study the reconstruction performance with respect to the data distribution and we propose the use of nonuniform probabilities for the randomised updates. Our simulations show the feasibility of the randomisation given a limited computing infrastructure as well as important computational advantages when compared to state-of-the-art algorithmic structures.

关键词： primal-dual algorithm Image processing Radio interferometry radiowave interferometry Image processing data distribution RADIO TELESCOPES RANDOMISING Distributed processing distributed algorithms Randomisation Square kilometre Dataset iterative methods

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A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting

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NUMERICAL algorithmS 2023年第1期93卷 103-130页

作者： Aragon-Artacho, Francisco J. Bot, Radu, I Torregrosa-Belen, David Univ Alicante Dept Math Alicante 03690 Spain Univ Vienna Fac Math A-1090 Vienna Austria

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.

关键词： Monotone operator Monotone inclusion Splitting algorithm primal-dual algorithm Minimal lifting

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An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems

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NUMERICAL algorithmS 2016年第3期71卷 519-540页

作者： Bot, Radu Ioan Csetnek, Ernoe Robert Univ Vienna Fac Math Oskar Morgenstern Pl 1 A-1090 Vienna Austria

We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian operator. By making use of the product space approach, we expand it to the solving of inclusion problems involving mixtures of linearly composed and parallel-sum type monotone operators. We obtain in this way an inertial forward-backward-forward primal-dual splitting algorithm having as main characteristic the fact that in the iterative scheme all operators are accessed separately either via forward or via backward evaluations. We present also the variational case when one is interested in the solving of a primal-dual pair of convex optimization problems with complexly structured objectives, which we also illustrate by numerical experiments in image processing.

关键词： Maximally monotone operator Resolvent Subdifferential Convex optimization Inertial splitting algorithm primal-dual algorithm

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Robust primal-dual Proximal algorithm for Cooperative Localization in WSNs 27

Robust Primal-Dual Proximal Algorithm for Cooperative Locali...

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27th International Conference on Information Fusion (FUSION)

作者： Zhang, Mei Shen, Xiaojing Wang, Zhiguo Varshney, Pramod K. Sichuan Univ Dept Math Chengdu Peoples R China Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY USA

ISBN: (纸本)9798350371420;9781737749769

This paper addresses the localization challenge in cooperative multi-agent wireless sensor networks, specifically focusing on range-based localization. To enhance robustness against outliers in range measurements, we employ the Huber function, leading to the formulation of a robust yet nonconvex optimization problem with coupled agent variables. Confronted with this nonconvex optimization challenge, particularly in large-scale networks, we reformulate the problem using Lagrange duality and conjugate theory. This restructuring yields subproblems characterized by smooth strong convexity for dual variables and a simplified form for primal variables, thereby facilitating an efficient solution. Building upon this reformulation, we introduce a novel distributed primal-dual algorithm that employs coordinate descent and proximal minimization techniques within an iterative framework. This approach furnishes closed-form solutions for both primal and dual variables. Theoretically, our method ensures not only the convergence of the sequence of objective function values but also, by leveraging the Kurdyka-Lojasiewicz property, we establish the guaranteed global convergence of the location estimates sequence to a critical point of the original objective function. Notably, our proposed approach exhibits lower computational complexity, communication cost, and storage space compared to existing methods. Numerical experiments underscore the superiority of the proposed method in terms of robustness and localization accuracy when compared to the other methods in the literature.

关键词： primal-dual algorithm Huber loss non-convex optimization wireless sensor network localization

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