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A Unified Bregman alternating minimization algorithm for Generalized DC Programs with Application to Imaging

JOURNAL OF SCIENTIFIC COMPUTING 2024年第3期101卷 76页

作者： He, Hongjin Zhang, Zhiyuan Ningbo Univ Sch Math & Stat Ningbo 315211 Peoples R China Southern Methodist Univ Dept Operat Res & Engn Management Dallas TX 75205 USA

In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized Difference-of-Convex functions (DC) programs, which is minimizing the sum of two separable DC parts and one two-block-variable coupling function. To circumvent the nonconvexity and nonseparability of the problem under consideration, we accordingly introduce a unified Bregman alternating minimization algorithm by maximally exploiting the favorable DC structure of the objective. Specifically, we first follow the spirit of alternating minimization to update each block variable in a sequential order, which can efficiently tackle the nonseparablitity caused by the coupling function. Then, we employ the Fenchel-Young inequality to approximate the second DC components (i.e., concave parts) so that each subproblem reduces to a convex optimization problem, thereby alleviating the computational burden of the nonconvex DC parts. Moreover, each subproblem absorbs a Bregman proximal regularization term, which is usually beneficial for inducing closed-form solutions of subproblems for many cases via choosing appropriate Bregman kernel functions. It is remarkable that our algorithm not only provides an algorithmic framework to understand the iterative schemes of some recently proposed algorithms, but also enjoys implementable schemes with easier subproblems than some state-of-the-art first-order algorithms developed for generic nonconvex and nonsmooth optimization problems. Theoretically, we prove that the sequence generated by our algorithm globally converges to a critical point under the Kurdyka-& Lstrok;ojasiewicz (K & Lstrok;) condition. Besides, we estimate the local convergence rates of our algorithm when we further know the prior information of the K & Lstrok;exponent. A series of numerical experiments on imaging data demonstrate the reliability and efficiency of the proposed algorithmic framework.

关键词： DC programs Nonconvex optimization Bregman distance alternating minimization algorithm First-order methods Kurdyka-& Lstrok ojasiewicz property Image processing

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Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle

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JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY 2018年第4期26卷 603-622页

作者： Wu, Junfeng Dai, Fang Hu, Gang Mou, Xuanqin Xian Univ Technol Coll Sci Xian 710048 Shaanxi Peoples R China Southeast Univ Key Lab Comp Network & Informat Integrat Minist Educ Nanjing Jiangsu Peoples R China Xi An Jiao Tong Univ Inst Image Proc & Pattern Recognit Xian Shaanxi Peoples R China

Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l(0)-norm dictionary learning regularization has been developed to reconstructCTimages from the lowdose and few-viewdataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l(0)-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l(1)norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l(0)-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.

关键词： L-1 norm dictionary learning alternating minimization algorithm balancing principle low dose CT reconstruction

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Line Integral alternating minimization algorithm for Dual-Energy X-Ray CT Image Reconstruction

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2016年第2期35卷 685-698页

作者： Chen, Yaqi O'Sullivan, Joseph A. Politte, David G. Evans, Joshua D. Han, Dong Whiting, Bruce R. Williamson, Jeffrey F. Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA Washington Univ Sch Med Mallinckrodt Inst Radiol Elect Radiol Lab St Louis MO 63110 USA Virginia Commonwealth Univ Dept Radiat Oncol Richmond VA 23220 USA Univ Pittsburgh Dept Radiol Pittsburgh PA 15213 USA

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

关键词： alternating minimization algorithm dual-energy iterative deblurring algorithm line integral X-ray CT

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alternating minimization differential privacy protection algorithm for the novel dual-mode learning tasks model

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 259卷

作者： Zhao, Pengfei Zhang, Kaili Zhang, Haibin Chen, Haibin Beijing Univ Civil Engn & Architecture Sch Civil & Transportat Engn Beijing 102616 Peoples R China Beijing 2 Middle Sch Beijing 100010 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Beijing Univ Technol Dept Operat Res & Informat Engn Beijing 100124 Peoples R China Qufu Normal Univ Sch Management Sci Rizhao 276800 Shandong Peoples R China Ctr Intelligent Multidimens Data Anal Shatin Hong Kong Sci Pk Hong Kong Peoples R China

The privacy-protected algorithm (PPA) is pivotal in the realm of machine learning, especially for handling sensitive data types, such as medical and financial records. PPA enables two distinct operations: data publishing and data analysis, each capable of functioning independently. However, the field lacks a unified framework or an efficient algorithm to synergize these operations. This deficiency inspires our current research endeavor. In this paper, we introduce a novel dual-mode empirical risk minimization (D-ERM) model, specifically designed for integrated learning tasks. We also develop an alternating minimization differential privacy protection algorithm (AMDPPA) for implementing the D-ERM model. Our theoretical analysis confirms the differential privacy and accuracy of AMDPPA. We validate the algorithm's efficacy through numerical experiments using real-world datasets, demonstrating its ability to effectively balance privacy with learning efficiency.

关键词： Differential privacy protection Dual-mode learning Dual-mode empirical risk minimization model alternating minimization algorithm

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A new alternating minimization algorithm for image segmentation

A new alternating minimization algorithm for image segmentat...

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6th International Conference on Wireless, Mobile and Multi-Media (ICWMMN 2015)

作者： Zeyang Dou Bin Zhang Xinyan Yu Department of Applied Mathematics Communication University of China Beijing China

ISBN: (纸本)9781510822030

A new alternating minimization algorithm for image segmentation is proposed. Based on the similarities between Ambrosio-Tortorelli model and Perona-Malik model, a new explicit alternating minimization algorithm is developed. The Euler-Lagrange equations of Ambrosio-Tortorelli model is modified to produce sharper edges. The effect of parameters is studied. Numerical results are presented to illustrate the effectiveness of the proposed model.

关键词： Image segmentation Ambrosio -Tortorelli model Perona-Malik model alternating minimization algorithm Explicit scheme image segmentation algorithms

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On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithms 6

On the convergence of adaptive first order methods: proximal...

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6th Annual Learning for Dynamics and Control Conference

作者： Latafat, Puya Themelis, Andreas Patrinos, Panagiotis Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS Kasteelpark Arenberg 10 B-3001 Leuven Belgium Kyushu Univ Fac Informat Sci & Elect Engn ISEE 744 MotookaNishi-Ku Fukuoka 8190395 Japan

Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes AdaPG(q,r), a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds. Different choices of the parameters q and r are discussed and the efficacy of the resulting methods is demonstrated through numerical simulations. In an attempt to better understand the underlying theory, its convergence is established in a more general setting that allows for time-varying parameters. Finally, an adaptive alternating minimization algorithm is presented by exploring the dual setting. This algorithm not only incorporates additional adaptivity, but also expands its applicability beyond standard strongly convex settings.

关键词： Convex minimization proximal gradient method alternating minimization algorithm locally Lipschitz gradient linesearch-free adaptive stepsizes

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Data-Driven Joint Distributionally Robust Chance-Constrained Operation for Multiple Integrated Electricity and Heating Systems

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2024年第3期15卷 1782-1798页

作者： Zhai, Junyi Jiang, Yuning Zhou, Ming Shi, Yuanming Chen, Wei Jones, Colin N. China Univ Petr East China Coll New Energy Qingdao 266580 Shandong Peoples R China Ecole Polytech Fed Lausanne Automat Control Lab CH-1015 Lausanne Switzerland North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100190 Peoples R China Tsinghua Univ Beijing Natl Res Ctr Informat Sci & Technol Beijing 100190 Peoples R China

Integrating heating and electricity networks offers extra flexibility to the energy system operation while improving energy utilization efficiency. This paper proposes a data-driven joint distributionally robust chance-constrained (DRCC) operation model for multiple integrated electricity and heating systems (IEHSs). Flexible reserve resources in IEHS are exploited to mitigate the uncertainty of renewable energy. A distributed and parallel joint DRCC operation framework is developed to preserve the decision-making independence of multiple IEHSs, where the optimized CVaR approximation (OCA) approach is developed to transform the local joint DRCC model into a tractable model. An alternating minimization algorithm is presented to improve the tightness of OCA for joint chance constraints by iteratively tuning the OCA. Case studies on the IEEE 33-bus system with four IEHSs and the IEEE 141-bus system with eight IEHSs demonstrate the effectiveness of the proposed approach.

关键词： Cogeneration Heating systems Uncertainty Resistance heating Pipelines Renewable energy sources Electricity alternating minimization algorithm data-driven distributed optimization integrated electricity and heating systems (IEHSs) joint distributionally robust chance-constrained optimized CVaR approximation (OCA)

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An Enhanced Regularized Clustering Method With Adaptive Spurious Connection Detection

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IEEE SIGNAL PROCESSING LETTERS 2023年 30卷 1332-1336页

作者： Chen, Huangyue Kong, Lingchen Qu, Wentao Xiu, Xianchao Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Beijing Jiaotong Univ Sch Math & Stat Beijing 100044 Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200444 Peoples R China

The regularized clustering (RC) framework based on the fusion penalty has attracted extensive attention in the last decade because it does not require the prior knowledge of the number of clusters. Although the ground truth connections and weights among samples are beneficial for clustering, the performance of RC could be distorted by the omnipresent spurious connections in real-world data sets. To effectively address the issue, this letter constructs an enhanced regularized clustering model by incorporating a spurious connection detection mechanism into the objective function of the RC framework. The proposed model can effectively reduce the damage caused by spurious connections through adaptively identifying the importance of each connection. Furthermore, an alternating minimization algorithm is developed with detailed convergence analysis. Experimental results validate its effectiveness against several state-of-the-art RC methods.

关键词： Clustering algorithms Signal processing algorithms Optimization Linear programming minimization Convergence Monitoring alternating minimization algorithm fusion penalty regularized clustering spurious connections

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A doubly sparse and low-patch-rank prior model for image restoration

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APPLIED MATHEMATICAL MODELLING 2022年 112卷 786-799页

作者： He, Hongjin Zhao, Lulu Ningbo Univ Sch Math & Stat Ningbo 315211 Peoples R China Fuzhou Univ Sch Math & Stat Fuzhou 350108 Peoples R China

Image restoration is a core problem in computer vision and image processing. In this paper, we introduce a unified low-patch-rank minimization model, which possesses one nuclear norm regularization term promoting the low-patch-rankness, and two sparse regulariza-tion terms including the classical total variation (TV) norm and a general sparse term un-der certain transform such as discrete cosine transform . By setting balancing parameters, our unified model reduces to the classical TV-regularized low-patch-rank minimization model and yields a new non-TV-regularized low-patch-rank prior image restoration model. Due to the multi-block structure of the model, we introduce a three-block alternating minimiza-tion algorithm to find approximate solutions of the proposed models. A series of compu-tational results on image inpainting and deblurring further show that our approaches are reliable to recover high-quality images from degraded ones. (c) 2022 Elsevier Inc. All rights reserved.

关键词： Total variation Discrete cosine transform Low-patch-rank Image inpainting Image deblurring alternating minimization algorithm

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Tensor Completion via A Generalized Transformed Tensor T-Product Decomposition Without t-SVD

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JOURNAL OF SCIENTIFIC COMPUTING 2022年第2期93卷 47-47页

作者： He, Hongjin Ling, Chen Xie, Wenhui Ningbo Univ Sch Math & Stat Ningbo 315211 Peoples R China Hangzhou Dianzi Univ Dept Math Hangzhou 310018 Peoples R China

Matrix and tensor nuclear norms have been successfully used to promote the low-rankness of tensors in low-rank tensor completion. However, singular value decomposition (SVD), which is computationally expensive for large-scale matrices, frequently appears in solving those nuclear norm minimization models. Based on the tensor-tensor product (T-product), in this paper, we first establish the equivalence between the so-called transformed tubal nuclear norm for a third-order tensor and the minimum of the sum of two factor tensors' squared Frobenius norms under a general invertible linear transform. Gainfully, we introduce a mode-unfolding (often named as "spatio-temporal" in the internet traffic data recovery literature) regularized tensor completion model that is able to efficiently exploit the hidden structures of tensors. Then, we propose an implementable alternating minimization algorithm to solve the underlying optimization model. It is remarkable that our approach does not require any SVDs and all subproblems of our algorithm enjoy closed-form solutions. A series of numerical experiments on traffic data recovery, color images and videos inpainting demonstrate that our SVD-free approach takes less computing time to achieve satisfactory accuracy than some state-of-the-art tensor nuclear norm minimization approaches.

关键词： Tensor completion Tensor-tensor product t-SVD Tubal rank Transformed tubal nuclear norm alternating minimization algorithm

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