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Inpainting by Flexible Haar-Wavelet Shrinkage

SIAM JOURNAL ON IMAGING SCIENCES 2008年第3期1卷 273-293页

作者： Chan, R. H. Setzer, S. Steidl, G. Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China Univ Mannheim Dept Math & Comp Sci D-68131 Mannheim Germany

We present novel wavelet-based inpainting algorithms. Applying ideas from anisotropic regularization and diffusion, our models can better handle degraded pixels at edges. We interpret our algorithms within the framework of forward-backward splitting methods in convex analysis and prove that the conditions for ensuring their convergence are fulfilled. Numerical examples illustrate the good performance of our algorithms.

关键词： image inpainting anisotropic methods forward-backward algorithm wavelet shrinkage

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A Hidden Semi-Markov Model with Duration-Dependent State Transition Probabilities for Prognostics

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-10页

作者： Wang, Ning Sun, Shu-dong Cai, Zhi-qiang Zhang, Shuai Saygin, Can Changan Univ Dept Automobile Xian 710064 Peoples R China Northwestern Polytech Univ Dept Ind Engn Xian 710072 Peoples R China Univ Texas San Antonio Dept Mech Engn San Antonio TX 78249 USA

Realistic prognostic tools are essential for effective condition-based maintenance systems. In this paper, a Duration-Dependent Hidden Semi-Markov Model (DD-HSMM) is proposed, which overcomes the shortcomings of traditional Hidden Markov Models (HMM), including the Hidden Semi-Markov Model (HSMM): (1) it allows explicit modeling of state transition probabilities between the states;(2) it relaxes observations' independence assumption by accommodating a connection between consecutive observations;and (3) it does not follow the unrealistic Markov chain's memoryless assumption and therefore it provides a more powerful modeling and analysis capability for real world problems. To facilitate the computation of the proposed DD-HSMM methodology, new forward-backward algorithm is developed. The demonstration and evaluation of the proposed methodology is carried out through a case study. The experimental results show that the DD-HSMM methodology is effective for equipment health monitoring and management.

关键词： MARKOV processes PROBABILITY theory forward-backward algorithm PROGNOSTIC tests MEMORYLESS systems

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Construction of Binary Multi-grid Markov Random Field Prior Models from Training Images

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MATHEMATICAL GEOSCIENCES 2013年第4期45卷 383-409页

作者： Toftaker, Hakon Tjelmeland, Hakon Norwegian Univ Sci & Technol NTNU Dept Math Sci Trondheim Norway

Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach for the construction of prior models for binary variables. On each grid level we adopt a Markov random field (MRF) conditioned on values in previous levels. Parameter estimation in MRFs is complicated by a computationally intractable normalizing constant. To cope with this problem, we generate a partially ordered Markov model (POMM) approximation to the MRF and use this in the model fitting procedure. Approximate unconditional simulation from the fitted model can easily be done by again adopting the POMM approximation to the fitted MRF. Approximate conditional simulation, for a given and easy to compute likelihood function, can also be performed either by the Metropolis-Hastings algorithm based on an approximation to the fitted MRF or by constructing a new POMM approximation to this approximate conditional distribution. The proposed methods are illustrated using three frequently used binary training images.

关键词： Markov random field forward-backward algorithm Multi-grid Facies modeling Maximum likelihood

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Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces

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OPTIMIZATION METHODS & SOFTWARE 2019年第3期34卷 489-514页

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

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve strong convergence, one usually needs to impose more restrictive properties for the involved operators, like strong monotonicity (respectively, strong convexity for optimization problems). In this paper, we propose a modified Krasnosel'skii-Mann algorithm in connection with the determination of a fixed point of a nonexpansive mapping and show strong convergence of the iteratively generated sequence to the minimal norm solution of the problem. Relying on this, we derive a forward-backward and a Douglas-Rachford algorithm, both endowed with Tikhonov regularization terms, which generate iterates that strongly converge to the minimal norm solution of the set of zeros of the sum of two maximally monotone operators. Furthermore, we formulate strong convergent primal-dual algorithms of forward-backward and Douglas-Rachford-type for highly structured monotone inclusion problems involving parallel-sums and compositions with linear operators. The resulting iterative schemes are particularized to the solving of convex minimization problems. The theoretical results are illustrated by numerical experiments on the split feasibility problem in infinite dimensional spaces.

关键词： fixed points of nonexpansive mappings Tikhonov regularization splitting methods forward-backward algorithm Douglas-Rachford algorithm primal-dual algorithm

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A modified inertial shrinking projection method for solving inclusion problems and quasi-nonexpansive multivalued mappings

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COMPUTATIONAL & APPLIED MATHEMATICS 2018年第5期37卷 5750-5774页

作者： Cholamjiak, Watcharaporn Pholasa, Nattawut Suantai, Suthep Univ Phayao Sch Sci Phayao 56000 Thailand Chiang Mai Univ Dept Math Ctr Excellence Math & Appl Math Fac Sci Chiang Mai 50200 Thailand

In this work, we propose a modified inertial and forward-backward splitting method for solving the fixed point problem of a quasi-nonexpansive multivalued mapping and the inclusion problem. Then, we establish the weak convergence theorem of the proposed method. The strongly convergent theorem is also established under suitable assumptions in Hilbert spaces using the shrinking projection method. Some preliminary numerical experiments are tested to illustrate the advantage performance of our methods.

关键词： Inertial method Inclusion problem Maximal monotone operator forward-backward algorithm Quasi-nonexpansive mapping 47J22 47H04 47H05 47H10

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Inversion of well logs into facies accounting for spatial dependencies and convolution effects

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2015年 134卷 237-246页

作者： Lindberg, D. V. Rimstad, E. Omre, H. Norwegian Univ Sci & Technol Dept Math Sci N-7491 Trondheim Norway Statoil ASA N-9481 Harstad Norway

We predict facies from wireline well log data for a fluvial deposit system offshore Norway. The wireline well logs used are sonic, gamma ray, neutron porosity, bulk density and resistivity. We solve this inverse problem in a predictive Bayesian setting, and perform the associated model parameter estimation. Spatial vertical structure of the facies is included in the model by a Markov chain assumption, making geological model interpretation possible. We also take convolution effect into account, assuming that the observed logs might be measured as a weighted sum of properties over a facies interval. We apply the methods On real well data, with thick facies layers inferred from core samples. The proposed facies classification model is compared to a naive Bayesian classifier, which does not take into account neither vertical spatial dependency, dependencies between the wireline well logs nor convolution effect. Results from a blind well indicate that facies predictions from our model are more reliable than predictions from the naive model in terms of correct facies classification and predicted layer thickness. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Bayesian categorical inversion Hidden Markov models Deconvolution forward-backward algorithm

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VLSI architectures for the MAP algorithm

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IEEE TRANSACTIONS ON COMMUNICATIONS 2003年第2期51卷 175-185页

作者： Boutillon, E Gross, WJ Gulak, PG Univ Bretagne Sud LESTER F-56325 Lorient France Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada

This paper presents several techniques for the very large-scale integration (VLSI) implementation of the maximum a posteriori (MAP) algorithm. In general, knowledge about the implementation of the Viterbi algorithm can be applied to the MAP algorithm. Bounds are derived for the dynamic range of the state metrics which enable the designer to optimize the word length. The computational kernel of the algorithm is the Add-MAX* operation, which is the Add-Compare-Select operation of the Viterbi algorithm with an added offset. We show that the critical path of the algorithm can be reduced if the Add-MAX* operation is reordered into an Offset-Add-Compare-Select operation by adjusting the location of registers. A general scheduling for the MAP algorithm is presented which gives the tradeoffs between computational complexity, latency, and memory size. Some of these architectures eliminate the need for RAM blocks with unusual form factors or can replace the RAM with registers. These architectures are suited to VLSI implementation of turbo decoders.

关键词： forward-backward algorithm MAP estimation turbo codes very large-scale integration (VLSI) Viterbi decoding

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Semiparametric hidden Markov model with non-parametric regression

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2018年第21期47卷 5196-5204页

作者： Huang, Mian Ji, Qinghua Yao, Weixin Shanghai Univ Finance & Econ Sch Stat & Management Shanghai Peoples R China Univ Calif Riverside Dept Stat Riverside CA 92521 USA

The hidden Markov model regression (HMMR) has been popularly used in many fields such as gene expression and activity recognition. However, the traditional HMMR requires the strong linearity assumption for the emission model. In this article, we propose a hidden Markov model with non-parametric regression (HMM-NR), where the mean and variance of emission model are unknown smooth functions. The new semiparametric model might greatly reduce the modeling bias and thus enhance the applicability of the traditional hidden Markov model regression. We propose an estimation procedure for the transition probability matrix and the non-parametric mean and variance functions by combining the ideas of the EM algorithm and the kernel regression. Simulation studies and a real data set application are used to demonstrate the effectiveness of the new estimation procedure.

关键词： EM algorithm forward-backward algorithm hidden Markov model regression kernel regression

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Convergence analysis and applications of the inertial algorithm solving inclusion problems

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APPLIED NUMERICAL MATHEMATICS 2022年 175卷 1-17页

作者： Tang, Yan Lin, Honghua Gibali, Aviv Cho, Yeol Je Chongqing Technol & Business Univ Sch Math & Stat Chongqing 400067 Peoples R China Sichuan Univ Coll Math Chengdu 610065 Peoples R China Southwest Univ Polit Sci & Law Business Sch Chongqing 401120 Peoples R China ORT Braude Coll Dept Math IL-2161002 Karmiel Israel Univ Haifa Ctr Math & Sci Computat Mt Carmel Haifa 3498838 Israel Gyeongsang Natl Univ Dept Math Educ Jinju 52828 South Korea China Med Univ Ctr Gen Educ Taichung 40402 Taiwan

Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more. In this work we are concern with the problem of finding a common solution of a monotone operator equation and fixed point of a nonexpansive mapping in real Hilbert spaces. Derived from dynamical systems, a simple inertial forward-backward splitting method for solving the problem is presented and analyzed under mild and standard assumptions. Some numerical examples in real-world and comparisons with related works, illustrate the theoretical advantages as well the potential applicability of the proposed scheme. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Monotone operator equation Fixed point forward-backward algorithm Inertial technique Nonexpansive mapping

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Optimization of HMM by the tabu search algorithm

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JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 2004年第5期20卷 949-957页

作者： Chen, TY Mei, XD Pan, JS Sun, SH Natl Kaohsiung Univ Appl Sci Dept Elect Engn Kaohsiung 807 Taiwan Harbin Inst Technol Dept Automat Test Measurement & Control Harbin 150001 Peoples R China

In this paper, a simple version of the tabu search algorithm is employed to train a Hidden Markov Model (HMM) to search out the optimal parameter structure of HMM for automatic speech recognition. The proposed TS-HMM training provides a mechanism that allows the search process to escape from a local optimum and obtain a near global optimum. Experimental results show that the TS-HMM training has a higher probability of finding the optimal model parameters than traditional algorithms do.

关键词： tabu search hidden Markov model forward-backward algorithm speech recognition global optimum

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