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A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially Varying Generalised Gaussian Models

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2024年第4期66卷 550-571页

作者： Chouzenoux, Emilie Corbineau, Marie-Caroline Pesquet, Jean-Christophe Scrivanti, Gabriele Univ Paris Saclay Inria Cent Supelec CVN Gif Sur Yvette France Preligens Res Dept Paris France

The joint problem of reconstruction/feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly propose a novel non-smooth and non-convex variational formulation of the problem. For this purpose, we introduce a versatile generalised Gaussian prior whose parameters, including its exponent, are space-variant. Secondly, we design an alternating proximal-based optimisation algorithm that efficiently exploits the structure of the proposed non-convex objective function. We also analyse the convergence of this algorithm. As shown in numerical experiments conducted on joint deblurring/segmentation tasks, the proposed method provides high-quality results.

关键词： Image recovery Space-variant regularisation Alternating minimisation proximal algorithm Block coordinate descent Image segmentation

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Computation for Latent Variable Model Estimation: A Unified Stochastic proximal Framework

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PSYCHOMETRIKA 2022年第4期87卷 1473-1502页

作者： Zhang, Siliang Chen, Yunxiao East China Normal Univ Shanghai Peoples R China London Sch Econ & Polit Sci London England

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of many latent variables, (2) the observed and latent variables being continuous, discrete, or a combination of both, (3) constraints on parameters, and (4) penalties on parameters to impose model parsimony. The estimation often involves maximizing an objective function based on a marginal likelihood/pseudo-likelihood, possibly with constraints and/or penalties on parameters. Solving this optimization problem is highly non-trivial, due to the complexities brought by the features mentioned above. Although several efficient algorithms have been proposed, there lacks a unified computational framework that takes all these features into account. In this paper, we fill the gap. Specifically, we provide a unified formulation for the optimization problem and then propose a quasi-Newton stochastic proximal algorithm. Theoretical properties of the proposed algorithms are established. The computational efficiency and robustness are shown by simulation studies under various settings for latent variable model estimation.

关键词： latent variable models penalized estimator stochastic approximation proximal algorithm quasi-Newton methods Polyak-Ruppert averaging

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Tensor Robust Principal Component Analysis From Multilevel Quantized Observations

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第1期69卷 383-406页

作者： Wang, Jianjun Hou, Jingyao Eldar, Yonina C. C. Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China China West Normal Univ Coll Math & Informat Nanchong 637002 Sichuan Peoples R China Weizmann Inst Sci Fac Math & Comp Sci IL-7610001 Rehovot Israel

We consider Quantized Tensor Robust Principal Component Analysis (Q-TRPCA), which aims to recover a low-rank tensor and a sparse tensor from noisy, quantized, and sparsely corrupted measurements. A nonconvex constrained maximum likelihood (ML) estimation method is proposed for Q-TRPCA. We provide an upper bound on the Frobenius norm of tensor estimation error under this method. Making use of tools in information theory, we derive a theoretical lower bound on the best achievable estimation error from unquantized measurements. Compared with the lower bound, the upper bound on the estimation error is nearly order-optimal. We further develop an efficient convex ML estimation scheme for Q-TRPCA based on the tensor nuclear norm (TNN) constraint. This method is more robust to sparse noises than the latter nonconvex ML estimation approach. Conducting experiments on both synthetic data and real-world data, we show the effectiveness of the proposed methods.

关键词： Tensors Sparse matrices Quantization (signal) Principal component analysis Matrix decomposition Optimization Maximum likelihood estimation Low-tubal-rank tensor maximum likelihood estimation multi-level quantization proximal algorithm

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A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第2期198卷 857-867页

作者： Crouzeix, Jean-Pierre Hassouni, Abdelhak Ocana, Eladio Univ Clermont Auvergne LIMOS 1 Rue Chebarde F-63178 Aubiere France Univ Mohammed 5 Fac Sci BP 1014 Rabat Morocco Univ Nacl Ingn IMCA Inst Matemat & Ciencias Afines Calle Biologos 245 Urb San Cesar Lima Peru

The main result concerns the second-order differentiability of the marginal function of a convex twice differentiable function. The inf-convolution and the proximal algorithm are revised according to the result as exa... 详细信息

关键词： Convex analysis Convex duality Conjugacy Marginal function Inf-convolution proximal algorithm

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A connection between Chidume iteration and the contraction-proximal point algorithm

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AFRIKA MATEMATIKA 2015年第1-2期26卷 127-130页

作者： Moudafi, Abdellatif French West Indies Univ Ceregmia DSI Schoelcher Martinique France

In this short note we comment on some recent results on the convergence of two type of iterative algorithms for finding a zero of a maximal monotone operator. The first one is based on a proximal approach and was investigated by many authors, see for example (Boikanyo and Morosanu in Nonlinear Anal TMA 74:544-555, 2011;Kamimura and Takahashi in J Approx Theory 106:226-240, 2(X)0, Marino and Xu in Comm Pure Appl Anal 3:791-808, 2004, Wang and Cui in J Global Optim 54:485-491, 2012, Yao and Noor in J Comput Appl Math 217:46-55, 2008) and the references therein. The second is based on a gradient approach and was essentially developed by Chidume et al. see for instance (Fixed Point Theory 2013, Chidume and Djitte in Abst Appl Anal doi:10.1155/2012/681348 2012, Chidume et al. in J Nonlinear Cony Anal (to appear) 2013, Ofoedu and Zegeye in J Math Anal Appl 372:68-76, 2010) and the references therein. Then, relying on the Yosida approximate, we compare and make a link between these two approaches.

关键词： Maximal monotone operators Gradient method proximal algorithm Regularization Yosida approximate Strong convergence

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Scalable proximal methods for cause-specific hazard modeling with time-varying coefficients

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LIFETIME DATA ANALYSIS 2022年第2期28卷 194-218页

作者： Wu, Wenbo Taylor, Jeremy M. G. Brouwer, Andrew F. Luo, Lingfeng Kang, Jian Jiang, Hui He, Kevin Univ Michigan Dept Biostat 1420 Washington Hts Ann Arbor MI 48109 USA Univ Michigan Dept Epidemiol 1420 Washington Hts Ann Arbor MI 48109 USA

Survival modeling with time-varying coefficients has proven useful in analyzing time-to-event data with one or more distinct failure types. When studying the cause-specific etiology of breast and prostate cancers using the large-scale data from the Surveillance, Epidemiology, and End Results (SEER) Program, we encountered two major challenges that existing methods for estimating time-varying coefficients cannot tackle. First, these methods, dependent on expanding the original data in a repeated measurement format, result in formidable time and memory consumption as the sample size escalates to over one million. In this case, even a well-configured workstation cannot accommodate their implementations. Second, when the large-scale data under analysis include binary predictors with near-zero variance (e.g., only 0.6% of patients in our SEER prostate cancer data had tumors regional to the lymph nodes), existing methods suffer from numerical instability due to ill-conditioned second-order information. The estimation accuracy deteriorates further with multiple competing risks. To address these issues, we propose a proximal Newton algorithm with a shared-memory parallelization scheme and tests of significance and nonproportionality for the time-varying effects. A simulation study shows that our scalable approach reduces the time and memory costs by orders of magnitude and enjoys improved estimation accuracy compared with alternative approaches. Applications to the SEER cancer data demonstrate the real-world performance of the proximal Newton algorithm.

关键词： Kronecker product B-spline proximal algorithm Parallel computing Breast cancer Prostate cancer

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A model-based variable step-size strategy for proximal multitask diffusion LMS algorithm

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DIGITAL SIGNAL PROCESSING 2021年 117卷 103199-103199页

作者： Zhang, Yuge Jin, Danqi Chen, Jie Northwestern Polytech Univ Sch Marine Sci & Technol Ctr Intelligent Acoust & Immers Commun Xian Peoples R China

Several practical applications, such as distributed spectrum sensing and channel identification in underwater communication networks with multiple sensors, can be modeled as a distributed network with jointly sparse structure. For such a network, the proximal multitask diffusion least mean square (LMS) algorithm has been proposed in the literature, and its performance has been studied thoroughly. Due to the trade-off between convergence speed and steady-state performance in the proximal multitask diffusion LMS algorithm, it is important but not trivial, to set the step-size parameter properly. To address this issue, a variable step-size strategy for the proximal multitask diffusion LMS algorithm is proposed in this paper. Based on the transient model of the proximal multitask diffusion LMS algorithm, and by minimizing an upper-bound of the excess mean-square error (EMSE) at each iteration on the basis of a white input assumption, we obtain a closed-form expression of the step-size parameter. Simulation results illustrate the effectiveness of the proposed strategy and highlight its performance through comparison with other existing variable step-size strategies, in the cases of white and moderately correlated inputs. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Distributed optimization Diffusion strategy Variable step-size strategy proximal algorithm Transient model

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Distributed Optimization With Coupling Constraints

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第3期68卷 1847-1854页

作者： Wu, Xuyang Wang, He Lu, Jie KTH Royal Inst Technol Div Decis & Control Syst SE-10044 Stockholm Sweden ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China

In this article, we investigate distributed convex opti-mization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the constraints can be both sparsely and densely cou-pling. By strategically integrating ideas from primal-dual, proxi-mal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the prob-lem over a connected, undirected graph. We show that IPLUX achieves an O(1/k) rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation.

关键词： Convergence Couplings Optimization Convex functions Linear programming Distributed algorithms Transforms Constrained optimization distributed optimization primal-dual method proximal algorithm

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Relaxed inertial methods for solving the split monotone variational inclusion problem beyond co-coerciveness

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OPTIMIZATION 2023年第2期72卷 607-646页

作者： Izuchukwu, Chinedu Reich, Simeon Shehu, Yekini Technion Israel Inst Technol Dept Math Haifa Israel Zhejiang Normal Univ Dept Math Jinhua Zhejiang Peoples R China

We study the split monotone variational inclusion problem in two real Hilbert spaces. Combining the inertial and relaxation techniques with the proximal contraction algorithm, we propose two new methods for solving th... 详细信息

关键词： Contraction method Lipschitz continuous monotone opearator proximal algorithm relaxed inertial method split monotone variational inclusion problem

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Joint decomposition of multichannel signals with multimarginal optimal transport 32

Joint decomposition of multichannel signals with multimargin...

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32nd European Signal Processing Conference (EUSIPCO)

作者： Mallejac, Jean Idier, Jerome Soussen, Charles Li, Xiangyi Univ Paris Saclay CentraleSupelec CNRS L2S F-91192 Gif Sur Yvette France Nantes Univ Ecole Cent Nantes CNRS LS2N F-44000 Nantes France Aix Marseille Univ Cent Marseille CNRS Inst Fresnel F-13013 Marseille France

ISBN: (纸本)9789464593617;9798331519773

The joint decomposition of a sequence of signals is addressed, where each signal is coded within a predefined dictionary. We propose a convex variational formulation involving a regularization term based on optimal transport. The latter is designed so as to promote proximity between neighboring channels. Two kinds of regularization criteria are designed, corresponding to distinct cross-channel information on the transport of dictionary atoms from one channel to another. The resulting optimization problems are reformulated as quadratic programs and solved using a proximal algorithm. The proposed approach is analyzed for a multichannel deconvolution problem.

关键词： Inverse problem multichannel decomposition optimal transport proximal algorithm

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