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Sequence Detection algorithms for PHY-Layer Sensing in Dynamic Spectrum Access Networks

IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2011年第1期5卷 97-109页

作者： Sun, Zhanwei Bradford, Glenn J. Laneman, J. Nicholas Univ Notre Dame Dept Elect Engn Notre Dame IN 46556 USA

Spectrum sensing is a critical function for enabling dynamic spectrum access (DSA) in wireless networks that utilize cognitive radio (CR). In DSA networks, unlicensed secondary users can gain access to a licensed spectrum band as long as they do not cause harmful interfere to primary users. Spectrum sensing is subject to errors in the form of false alarms and missed detections. False alarms cause spectrum under-use by secondary users, and missed detections cause interference to primary users. Although existing research has demonstrated the utility of a Markov chain for modeling the spectrum access pattern of primary users over time, little effort has been directed toward spectrum sensing based upon such models. In this paper, we develop general sequence detection algorithms for Markov sources in noise for spectrum sensing in DSA networks. We assign different Bayesian cost factors for missed detections and false alarms, and we show that a suitably modified forward-backward sequence detection algorithm is optimal in minimizing the detection risk. Two advanced sequence detection algorithms, the complete forward algorithm and the complete forward partial backward algorithm are introduced and their performances are compared as well. Along the way, we observe new fundamental limitations on sensing performance that we term the risk floor and the window length limitation of energy detection and coherent detection that arise from mismatch of their observation window with the PU's spectrum access pattern.

关键词： Cognitive radio (CR) dynamic spectrum access (DSA) forward-backward algorithm hidden Markov model (HMM) spectrum sensing Viterbi algorithm

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Gradient computation in linear-chain conditional random fields using the entropy message passing algorithm

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PATTERN RECOGNITION LETTERS 2012年第13期33卷 1776-1784页

作者： Ilic, Velimir M. Mancev, Dejan I. Todorovic, Branimir T. Stankovic, Miomir S. Serbian Acad Arts & Sci Math Inst Belgrade 11000 Serbia Univ Nis Fac Sci & Math Nish 18000 Serbia Univ Nis Fac Occupat Safety Nish 18000 Serbia

The paper proposes a numerically stable recursive algorithm for the exact computation of the linear-chain conditional random field gradient. It operates as a forward algorithm over the log-domain expectation semiring and has the purpose of enhancing memory efficiency when applied to long observation sequences. Unlike the traditional algorithm based on the forward-backward recursions, the memory complexity of our algorithm does not depend on the sequence length. The experiments on real data show that it can be useful for the problems which deal with long sequences. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Conditional random fields Expectation semiring forward-backward algorithm Gradient computation Graphical models Message passing

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Diagnosis and Prognosis of Degradation Process via Hidden Semi-Markov Model

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IEEE-ASME TRANSACTIONS ON MECHATRONICS 2018年第3期23卷 1456-1466页

作者： Liu, Tongshun Zhu, Kunpeng Zeng, Liangcai Univ Sci & Technol China Dept Automat Hefei 230026 Anhui Peoples R China Chinese Acad Sci Hefei Inst Phys Sci Inst Adv Mfg Technol Changzhou 213164 Peoples R China Wuhan Univ Sci & Technol Sch Machinery & Automat Wuhan 430081 Hubei Peoples R China

The intelligent estimation of degradation state and the prediction of remaining useful life (RUL) are important for the maintenance of industrial equipment. In this study, the degradation process of equipment is modeled as an improved hidden semi-Markov model (HSMM), in which the dependence of durations of adjacent degradation states is described and modeled in the HSMM. To avoid underflow problem in computing the forward and backward variables, a modified forward-backward algorithm is proposed in the HSMM. Based on the improved algorithm, online estimation of degradation state and the distribution of RUL can be obtained. Case studies on tool wearing diagnosis and prognosis have verified the effectiveness of this model.

关键词： Degradation process forward-backward algorithm health monitoring Hidden semi-Markov remaining useful life (RUL)

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A hidden semi-Markov model with missing data and multiple observation sequences for mobility tracking

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SIGNAL PROCESSING 2003年第2期83卷 235-250页

作者： Yu, SZ Kobayashi, H Princeton Univ Dept Elect Engn Princeton NJ 08544 USA

A hidden Markov model (HMM) encompasses a large class of stochastic process models and has been successfully applied to a number of scientific and engineering problems, including speech and other pattern recognition problems, and DNA sequence comparison. A hidden semi-Markov model (HSMM) is an extension of HMM, designed to remove the constant or geometric distributions of the state durations assumed in HMM. A larger class of practical problems can be appropriately modeled in the setting of HSMM. A major restriction is found, however, in both conventional HMM and HSMM, i.e., it is generally assumed that there exists at least one observation associated with every state that the hidden Markov chain takes on. We will remove this assumption and consider the following situations: (i) observation data may be missing for some intervals;and (ii) there are multiple observation streams that are not necessarily synchronous to each other and may have different "emission distributions" for the same state. We propose a new and computationally efficient forward-backward algorithm for HSMM with missing observations and multiple observation sequences. The required computational amount for the forward and backward variables is reduced to O(D), where D is the maximum allowed duration in a state. Finally, we will apply the extended HSMM to estimate the mobility model parameters for the Internet service provisioning in wireless networks. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： hidden Markov model (HMM) HMM with explicit duration hidden semi-Markov Model (HSMM) missing data multiple observations Ferguson algorithm forward-backward algorithm expectation-maximization (EM) algorithm maximum likelihood (ML) estimation maximum a posteriori probability (MAP) estimation mobility modeling wireless Internet service

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A Bayesian Approach to Recurrence in Neural Networks

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2021年第8期43卷 2527-2537页

作者： Garner, Philip N. Tong, Sibo Idiap Res Inst CH-1920 Martigny Switzerland

We begin by reiterating that common neural network activation functions have simple Bayesian origins. In this spirit, we go on to show that Bayes's theorem also implies a simple recurrence relation;this leads to a Bayesian recurrent unit with a prescribed feedback formulation. We show that introduction of a context indicator leads to a variable feedback that is similar to the forget mechanism in conventional recurrent units. A similar approach leads to a probabilistic input gate. The Bayesian formulation leads naturally to the two pass algorithm of the Kalman smoother or forward-backward algorithm, meaning that inference naturally depends upon future inputs as well as past ones. Experiments on speech recognition confirm that the resulting architecture can perform as well as a bidirectional recurrent network with the same number of parameters as a unidirectional one. Further, when configured explicitly bidirectionally, the architecture can exceed the performance of a conventional bidirectional recurrence.

关键词： Logic gates Probabilistic logic Bayes methods Signal processing algorithms Hidden Markov models Training Computer architecture Neural networks bayesian statistics recurrence forward-backward algorithm speech recognition bidirectional LSTM

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Measuring the Influence of Observations in HMMs Through the Kullback-Leibler Distance

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IEEE SIGNAL PROCESSING LETTERS 2013年第2期20卷 145-148页

作者： Perduca, Vittorio Nuel, Gregory Univ Paris 05 Lab MAP5 Sorbonne Paris Cite France CNRS Sorbonne Paris Cite France

We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states' chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting meaningful observations} in HMM data series.

关键词： forward-backward algorithm Hidden Markov Models local outlier factor outlier detection relative entropy

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Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration

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OPTIMIZATION METHODS & SOFTWARE 2022年第6期37卷 2225-2240页

作者： Cheval, Horaiu Leustean, Laureniu Univ Bucharest Fac Math & Comp Sci Res Ctr Log Optimizat & Secur LOS Dept Comp Sci Acad 14 Bucharest 010014 Romania Romanian Acad Simion Stoilow Inst Math Calea Grivitei 21 Bucharest 010702 Romania

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bo, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas-Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov-Mann iteration.

关键词： Mann iteration Tikhonov regularization rates of asymptotic regularity Douglas-Rachford algorithm forward-backward algorithm proof mining

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Turbo Segmentation of Textured Images

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2011年第1期33卷 16-29页

作者： Lehmann, Frederic TELECOM SudParis Inst TELECOM Dept CITI F-91011 Evry France

We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.

关键词： Texture segmentation Markov random field hidden Markov autoregressive model factor graph forward-backward algorithm turbo processing

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Path partitions and forward-only trellis algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 2003年第1期49卷 38-52页

作者： Ma, X Kavcic, A Harvard Univ Div Engn & Appl Sci Cambridge MA 02138 USA

This is a semitutorial paper on trellis-based algorithms. We argue that most decoding/detection algorithms described on trellises can be formulated as path-partitioning algorithms, with proper definitions of mappings from subsets of paths to metrics of subsets. Thereby, the only two operations needed are path-concatenation and path-collection, which play the roles of multiplication and addition, respectively. Furthermore, we show that the trellis structure permits the path-partitioning algorithms to be formulated as forward-only algorithms (with structures resembling the Viterbi algorithm), thus eliminating the need for backward computations regardless of what task needs to be performed on the trellis. While all of the actual decoding/detection algorithms presented here are rederivations of variations of previously known methods, we believe that the exposition of the algorithms in a unified manner as forward-only path-partitioning algorithms is the most intuitive manner in which to generalize the Viterbi algorithm. We also believe that this approach may, in fact, influence the practical implementation of the algorithms as well as influence the construction of other forward-only algorithms (e.g., byte-wise forward-only detection algorithms).

关键词： Babl-Cocke-Jelinek-Raviv (BCJR) algorithm forward-backward algorithm forward-only algorithm Markov processes sum-product algorithm trellis graph Viterbi algorithm

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A Proximal Interior Point algorithm with Applications to Image Processing

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2020年第6-7期62卷 919-940页

作者： Chouzenoux, Emilie Corbineau, Marie-Caroline Pesquet, Jean-Christophe Univ Paris Saclay Inria Saclay Cent Supelec CVN 9 Rue Joliot Curie F-91190 Gif Sur Yvette France

In this article, we introduce a new proximal interior point algorithm (PIPA). This algorithm is able to handle convex optimization problems involving various constraints where the objective function is the sum of a Lipschitz differentiable term and a possibly nonsmooth one. Each iteration of PIPA involves the minimization of a merit function evaluated for decaying values of a logarithmic barrier parameter. This inner minimization is performed thanks to a finite number of subiterations of a variable metric forward-backward method employing a line search strategy. The convergence of this latter step as well as the convergence the global method itself is analyzed. The numerical efficiency of the proposed approach is demonstrated in two image processing applications.

关键词： Interior point methods Proximity operator Constrained optimization forward-backward algorithm Variable metric Line search Armijo strategy Hyperspectral unmixing Geometry-texture decomposition

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