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Asilomar Conference on Signals, Systems & Computers

作者： Farhang Vedadi Shahram Shirani Department of Electrical and Computer Engineering McMaster University Hamilton ONT Canada

ISBN: (纸本)9781467350501

De-interlacing is revisited as the problem of assigning a sequence of interpolation methods (interpolators) to a sequence of missing pixels of an interlaced frame (field). With this assumption, our algorithm undergoes transitions from one interpolator to another as it moves from one missing pixel position to the next one. We assume that the next state depends only on the current state which implies a first-order Markov-chain on the sequence of interpolators. For estimation of the optimum sequence of interpolators our algorithm introduces a novel cost function and then makes use of forward-backward algorithm to find the global optimum sequence of interpolators. Simulation results prove that the proposed method is superior to the well-known de-interlacing algorithms proposed in this field.

关键词： De-interlacing trellis diagrams forward-backward algorithm MAP estimation Markov chain model

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Simultaneous determination of wave velocity and thickness on overlapped signals using forward backward algorithm

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NDT & E INTERNATIONAL 2017年 86卷 100-105页

作者： Bustillo, J. Achdjian, H. Arciniegas, A. Blanc, L. Univ Francois Rabelais Tours CNRS INSA Ctr Val Loire GREMAN UMR 7347 Blois France

This paper presents a method to simultaneously determine the wave velocity and the thickness of an unknown sample in case of overlapped ultrasonic signals. Indeed, the determination of the time delay in an ultrasonic signal can be critical to allow the simultaneous characterization of parameters of the studied material, such as the thickness and the wave velocity. Therefore, a forward-backward algorithm is applied to the overlapped signal using a reference signal in order to retrieve the excitation signal. Firstly, the method is explained and a validation on synthetic signal is performed to observe its robustness. Secondly, a time retrieval is performed on real signals to determine thickness and wave velocity in aluminium plates. The results show that this method is suitable to simultaneously retrieve thickness and wave velocity, even for overlapped signals (up to 65%), with a discrepancy as low as 1%.

关键词： forward-backward algorithm Overlapping Simultaneous Ultrasonic

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A stochastic inertial forward-backward splitting algorithm for multivariate monotone inclusions

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OPTIMIZATION 2016年第6期65卷 1293-1314页

作者： Rosasco, Lorenzo Villa, Silvia Vu, Bang Cong Univ Genoa DIBRIS Genoa Italy Ist Italiano Tecnol LCSL Cambridge MA USA MIT 77 Massachusetts Ave Cambridge MA 02139 USA

We propose an inertial forward-backward splitting algorithm to compute a zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in real Hilbert spaces of the sequence of iterates to an optimal solution. Then, based on this analysis, we introduce two new classes of stochastic inertial primal-dual splitting methods for solving structured systems of composite monotone inclusions and prove their convergence. Our results extend to the stochastic and inertial setting various types of structured monotone inclusion problems and corresponding algorithmic solutions. Application to minimization problems is discussed.

关键词： Monotone inclusion monotone operator operator splitting cocoercive operator forward-backward algorithm composite operator duality primal-dual algorithm

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Three-step projected forward-backward algorithms for constrained minimization problem

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2025年第1期71卷 465-487页

作者： Kankam, Kunrada Noor, Muhammad Aslam Cholamjiak, Prasit Suan Dusit Univ Fac Educ Elementary Educ Program Lampang Ctr Lampang 52100 Thailand COMSATS Univ Islamabad Dept Math Islamabad Pakistan Univ Phayao Sch Sci Phayao 56000 Thailand

We design new projective forward-backward algorithms for constrained minimization problems. We then discuss its weak convergence via a new linesearch that the hypothesis on the Lipschitz constant of the gradient of functions is avoided. We provide its applications to solve image deblurring and image inpainting. Finally, we discuss the optimal selection of parameters that are proposed in algorithms in terms of PSNR and SSIM. It reveals that our new algorithm outperforms some recent methods introduced in the literature.

关键词： forward-backward algorithm Minimization problem Weak convergence Linesearch method

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Proximal algorithms for a Class of Abstract Convex Functions

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SET-VALUED AND VARIATIONAL ANALYSIS 2025年第1期33卷 1-44页

作者： Bednarczuk, Ewa Lorenz, Dirk Tran, The Hung Warsaw Univ Technol Fac Math & Informat Sci Koszykowa 75 PL-00662 Warsaw Poland Univ Bremen Ctr Ind Math Postfach 330440 D-28334 Bremen Germany PAS Syst Res Inst Dept Modeling & Optimizat Dynam Syst Newelska 6 PL-01447 Warsaw Poland

In this paper, we analyze a class of nonconvex optimization problems from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient, we propose an abstract notion of a proximal operator and derive several algorithms, namely abstract proximal point method, abstract forward-backward method, and abstract projected subgradient method. Global convergence results for all algorithms are discussed, and numerical examples are given.

关键词： Abstract convexity Proximal operator forward-backward algorithm Global convergence Proximal subgradient

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Novel forward-backward algorithms for optimization and applications to compressive sensing and image inpainting

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ADVANCES IN DIFFERENCE EQUATIONS 2021年第1期2021卷 1-22页

作者： Suantai, Suthep Noor, Muhammad Aslam Kankam, Kunrada Cholamjiak, Prasit Chiang Mai Univ Dept Math Data Sci Res Ctr Fac Sci Chiang Mai 50200 Thailand Chiang Mai Univ Dept Math Res Ctr Math & Appl Math Fac Sci Chiang Mai 50200 Thailand COMSATS Univ Islamabad Dept Math Islamabad Pakistan Univ Phayao Sch Sci Phayao 56000 Thailand

The forward-backward algorithm is a splitting method for solving convex minimization problems of the sum of two objective functions. It has a great attention in optimization due to its broad application to many disciplines, such as image and signal processing, optimal control, regression, and classification problems. In this work, we aim to introduce new forward-backward algorithms for solving both unconstrained and constrained convex minimization problems by using linesearch technique. We discuss the convergence under mild conditions that do not depend on the Lipschitz continuity assumption of the gradient. Finally, we provide some applications to solving compressive sensing and image inpainting problems. Numerical results show that the proposed algorithm is more efficient than some algorithms in the literature. We also discuss the optimal choice of parameters in algorithms via numerical experiments.

关键词： forward-backward algorithm Compressive sensing Image inpainting Minimization problem

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Convergence Results of forward-backward algorithms for Sum of Monotone Operators in Banach Spaces

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RESULTS IN MATHEMATICS 2019年第4期74卷 138-138页

作者： Shehu, Yekini IST Austria Campus 1 A-3400 Klosterneuburg Austria Zhejiang Normal Univ Dept Math Jinhua 321004 Zhejiang Peoples R China

It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper.

关键词： Inclusion problem 2-uniformly convex Banach space forward-backward algorithm weak convergence strong convergence

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forward-backward MULTIPLICITY CORRELATIONS IN RELATIVISTIC HEAVY-ION COLLISIONS

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ACTA PHYSICA POLONICA B 2015年第10期46卷 2039-2050页

作者： Bari, Waseem Gani, Qudsia Thoker, Shamsul H. Teli, Muzamil A. Univ Kashmir Dept Phys Srinagar 190006 Jammu & Kashmir India

This study presents the investigations on the occurrence of multiplicity correlations in the particle multiplicities in forward and backward hemisphere in the multiparticle states produced in 2 8 Si nuclei with various targets at two different energies. The forward-forward and forward-backward dispersions are looked into. The variation of the correlation strength as a function of the pseudorapidity range is investigated and its dependence on target mass as well as the incident energy is studied. In order to estimate the contribution of non-statistical fluctuations, we use the deviation of the value of effective cluster multiplicity from unity as the benchmark.

关键词： Particles (Nuclear physics) -- Multiplicity Relativistic quantum mechanics Heavy-ion atom collisions Fluctuations (Physics) forward-backward algorithm Particle size determination

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A Nonlinearly Preconditioned forward-backward Splitting Method and Applications

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2022年第16期42卷 1880-1895页

作者： Vu, Bang Cong Papadimitriou, Dimitri Huawei Belgium Res Ctr BeRC 3NLab Leuven Belgium

In this paper, we prove the weak convergence of the iterates generated by the nonlinearly preconditioned forward-backward splitting method for the sum of a maximally hypermonotone operator A and a hypercocoercive operator B under several suitable conditions. We provide several choices of the nonlinear preconditioners for solving nonlinearly composed inclusions. In particular, the backward-forward splitting method is recovered by the nonlinearly preconditioned forward-backward splitting method with a special choice of the nonlinear preconditioner.

关键词： Cocoercive composite operator forward-backward algorithm hypercocoercive hypermonotone monotone inclusion monotone operator operator splitting preconditioning

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Generalized forward-backward splitting with penalization for monotone inclusion problems

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第4期73卷 825-847页

作者： Nimana, Nimit Petrot, Narin Khon Kaen Univ Dept Math Fac Sci Khon Kaen 40002 Thailand Naresuan Univ Dept Math Fac Sci Phitsanulok 65000 Thailand Naresuan Univ Fac Sci Ctr Excellence Nonlinear Anal & Optimizat Phitsanulok 65000 Thailand

We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximally monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided that the condition corresponding to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong convergence of the iterates. Furthermore, we utilize the proposed method for minimizing a large-scale hierarchical minimization problem concerning the sum of differentiable and nondifferentiable convex functions subject to the set of minima of another differentiable convex function. We illustrate the functionality of the method through numerical experiments addressing constrained elastic net and generalized Heron location problems.

关键词： Monotone operator Monotone inclusion Hierarchical optimization forward-backward algorithm 47H05 65K05 65K10 90C25

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