• Title/Summary/Keyword: variational framework

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A Variational Framework for Single Image Dehazing Based on Restoration

  • Nan, Dong;Bi, Du-Yan;He, Lin-Yuan;Ma, Shi-Ping;Fan, Zun-Lin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.3
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    • pp.1182-1194
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    • 2016
  • The single image dehazing algorithm in existence can satisfy the demand only for improving either the effectiveness or efficiency. In order to solve the problem, a novel variational framework for single image dehazing based on restoration is proposed. Firstly, the initial atmospheric scattering model is transformed to meet the kimmel's Retinex variational model. Then, the green light component of image is considered as an input of the variational framework, which is generated by the sensitivity of green wavelength. Finally, the atmospheric transmission map is achieved by multi-resolution pyramid reduction to improve the visual effect of the results. Experimental results demonstrate that the proposed method can remove haze effectively with less memory consumption.

GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

  • Verma, Ram U.
    • Communications of the Korean Mathematical Society
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    • v.26 no.4
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    • pp.685-693
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    • 2011
  • General framework for proximal point algorithms based on the notion of (A, ${\eta}$)-maximal monotonicity (also referred to as (A, ${\eta}$)-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to (A, ${\eta}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

Convergence of an Iterative Algorithm for Systems of Variational Inequalities and Nonlinear Mappings in Banach Spaces

  • JEONG, JAE UG
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.933-951
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    • 2015
  • In this paper, we consider the problem of convergence of an iterative algorithm for a general system of variational inequalities, a nonexpansive mapping and an ${\eta}$-strictly pseudo-contractive mapping. Strong convergence theorems are established in the framework of real Banach spaces.

A Variational Numerical Method of Linear Elasticity through the Extended Framework of Hamilton's Principle (확장 해밀턴 이론에 근거한 선형탄성시스템의 변분동적수치해석법)

  • Kim, Jinkyu
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.1
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    • pp.37-43
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    • 2014
  • The extended framework of Hamilton's principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation. Based upon such framework, a new variational numerical method of linear elasticity is provided for the classical single-degree-of-freedom dynamical systems. For the undamped system, the algorithm is symplectic with respect to the time step. For the damped system, it is shown to be accurate with good convergence characteristics.

A NOTE ON THE GENERALIZED VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

  • Kum, Sangho
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.319-324
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    • 2009
  • In a series of papers [3, 4, 5], the author developed the generalized vector variational inequality with operator solutions (in short, GOVVI) by exploiting variational inequalities with operator solutions (in short, OVVI) due to Domokos and $Kolumb\acute{a}n$ [2]. In this note, we give an extension of the previous work [4] in the setting of Hausdorff locally convex spaces. To be more specific, we present an existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [7] within the framework of (GOVVI).

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A VARIANT OF THE GENERALIZED VECTOR VARIATIONAL INEQUALITY WITH OPERATOR SOLUTIONS

  • Kum, Sang-Ho
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.665-673
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    • 2006
  • In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

ON NONLINEAR VARIATIONAL INCLUSIONS WITH ($A,{\eta}$)-MONOTONE MAPPINGS

  • Hao, Yan
    • East Asian mathematical journal
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    • v.25 no.2
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    • pp.159-169
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    • 2009
  • In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, ${\eta}$)-monotone map-pings in the framework of Hilbert spaces. Based on the generalized resol-vent operator technique associated with (A, ${\eta}$)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, ${\eta}$)-monotonicity generalizes A-monotonicity and H-monotonicity, The results presented this paper improve and extend the corresponding results announced by many others.

Study on the Generalization of the Extended Framework of Hamilton's Principle in Transient Continua Problems (확장 해밀턴 이론의 일반화에 대한 고찰)

  • Kim, Jinkyu;Shin, Jinwon
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.29 no.5
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    • pp.421-428
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    • 2016
  • The present work extends the recent variational formulation to more general time-dependent problems. Thus, based upon recent works of variational formulation in dynamics and pure heat diffusion in the context of the extended framework of Hamilton's principle, formulation for fully coupled thermoelasticity is developed first, then, with thermoelasticity-poroelasticity analogy, poroelasticity formulation is provided. For each case, energy conservation and energy dissipation properties are discussed in Fourier transform domain.

Detecting Abnormal Human Movements Based on Variational Autoencoder

  • Doi Thi Lan;Seokhoon Yoon
    • International Journal of Internet, Broadcasting and Communication
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    • v.15 no.3
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    • pp.94-102
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    • 2023
  • Anomaly detection in human movements can improve safety in indoor workplaces. In this paper, we design a framework for detecting anomalous trajectories of humans in indoor spaces based on a variational autoencoder (VAE) with Bi-LSTM layers. First, the VAE is trained to capture the latent representation of normal trajectories. Then the abnormality of a new trajectory is checked using the trained VAE. In this step, the anomaly score of the trajectory is determined using the trajectory reconstruction error through the VAE. If the anomaly score exceeds a threshold, the trajectory is detected as an anomaly. To select the anomaly threshold, a new metric called D-score is proposed, which measures the difference between recall and precision. The anomaly threshold is selected according to the minimum value of the D-score on the validation set. The MIT Badge dataset, which is a real trajectory dataset of workers in indoor space, is used to evaluate the proposed framework. The experiment results show that our framework effectively identifies abnormal trajectories with 81.22% in terms of the F1-score.

A REMARK ON MULTI-VALUED GENERALIZED SYSTEM

  • Kum, Sangho
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.163-169
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    • 2011
  • Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.