Discrete Markov image modeling and inference on the quadtree

Noncasual Markov (or energy-based) models are widely used in early vision applications for the representation of images in high-dimensional inverse problems. Due to their noncausal nature, these models generally lead to iterative inference algorithms that are computationally demanding. In this paper, we consider a special class of nonlinear Markov models which allow one to circumvent this drawback. These models are defined as discrete Markov random fields (MRF) attached to the nodes of a quadtree. The quadtree induces causality properties which enable the design of exact, noniterative inference algorithms, similar to those used in the context of Markov chain models. We first introduce an extension of the Viterbi algorithm which enables exact maximum a posteriori (MAP) estimation on the quadtree. Two other algorithms, related to the MPM criterion and to Bouman and Shapiro's (1994) sequential-MAP (SMAP) estimator are derived on the same hierarchical structure. The estimation of the model hyper parameters is also addressed. Two expectation-maximization (EM)-type algorithms, allowing unsupervised inference with these models are defined. The practical relevance of the different models and inference algorithms is investigated in the context of image classification problem, on both synthetic and natural images.     

Expectation maximization algorithms for MAP estimation of jumpMarkov linear systems

In a jump Markov linear system, the state matrix, observation matrix, and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. Computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations. We present three expectation maximization (EM) algorithms for state estimation to compute maximum a posteriori (MAP) state sequence estimates [which are also known as Bayesian maximum likelihood state sequence estimates (MLSEs)]. The first EM algorithm yields the MAP estimate for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAP estimate of the (continuous) state of the jump linear system. The third EM algorithm computes the joint MAP estimate of the finite and continuous states. The three EM algorithms optimally combine a hidden Markov model (HMM) estimator and a Kalman smoother (KS) in three different ways to compute the desired MAP state sequence estimates. Unlike the conditional mean state estimates, which require computational cost exponential in the data length, the proposed iterative schemes are linear in the data length     

A Bayesian estimation approach for speech enhancement using hiddenMarkov models

A Bayesian estimation approach for enhancing speech signals which have been degraded by statistically independent additive noise is motivated and developed. In particular, minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators are developed using hidden Markov models (HMMs) for the clean signal and the noise process. It is shown that the MMSE estimator comprises a weighted sum of conditional mean estimators for the composite states of the noisy signal, where the weights equal the posterior probabilities of the composite states given the noisy signal. The estimation of several spectral functionals of the clean signal such as the sample spectrum and the complex exponential of the phase is also considered. A gain-adapted MAP estimator is developed using the expectation-maximization algorithm. The theoretical performance of the MMSE estimator is discussed, and convergence of the MAP estimator is proved. Both the MMSE and MAP estimators are tested in enhancing speech signals degraded by white Gaussian noise at input signal-to-noise ratios of from 5 to 20 dB     

Instantaneous Frequency Estimation of Nonlinear Frequency-Modulated Signals Under Strong Noise Environment

Instantaneous frequency (IF) is the most important parameter of a signal, which is an important representation of non-stationary signals, such as frequency-modulated signals. Usually, signals are received with noises. Under noise environment, the conventional IF estimation methods for nonlinear frequency-modulated (NLFM) signal cannot work. In this paper, we focus on how to extract IF of NLFM signal under strong noise environment. First, a modified S-method (SM) is proposed to represent the time–frequency (TF) characteristic. The modified SM uses an adaptive smooth window. The symmetric window is used for multi-component signals and asymmetric window for mono-component signals. The modified SM enhances the TF energy concentration and suppresses the cross-terms effectively. Then, the Viterbi algorithm is used to extract the IF from the TF plane. Viterbi algorithm is a hidden Markov chain approach, which is proposed here as the IF estimator. The proposed method is utilized for various types of NLFM signals. Simulation results demonstrate the efficiency and validity of the proposed method under strong noise environment.     

VLSI architectures for the MAP algorithm

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 (1967) 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.     

一种基于Viterbi算法的虚拟网络功能自适应部署方法

为了应对移动数据流量的爆炸性增长,5G移动通信网将引入新型的架构设计。软件定义网络和网络功能虚拟化是网络转型的关键技术,将驱动移动通信网络架构的创新,服务链虚拟网络功能的部署是网络虚拟化研究中亟待解决的问题。该文针对已有部署方法未考虑服务链中虚拟网络功能间顺序约束和移动业务特点的问题,提出一种基于Viterbi算法的虚拟网络功能自适应部署方法。该方法实时感知底层节点的资源变化并动态调整拓扑结构,采用隐马尔科夫模型描述满足资源约束的可用的底层网络节点拓扑信息,基于Viterbi算法在候选节点中选择时延最短的服务路径。实验表明,与其它的虚拟网络功能部署方法相比,该方法降低了服务链的服务处理时间,并提高了服务链的请求接受率和底层资源的成本效率。     

Batch and Sequential Bayesian Estimators of the Number of Active Terminals in an IEEE 802.11 Network

The performance of the IEEE 802.11 protocol based on the distributed coordination function (DCF) has been shown to be dependent on the number of competing terminals and the backoff parameters. Better performance can be expected if the parameters are adapted to the number of active users. In this paper we develop both off-line and online Bayesian signal processing algorithms to estimate the number of competing terminals. The estimation is based on the observed use of the channel and the number of competing terminals is modeled as a Markov chain with unknown transition matrix. The off-line estimator makes use of the Gibbs sampler whereas the first online estimator is based on the sequential Monte Carlo (SMC) technique. A deterministic variant of the SMC estimator is then developed, which is simpler to implement and offers superior performance. Finally a novel approximate maximum a posteriori (MAP) algorithm for hidden Markov models (HMM) with unknown transition matrix is proposed. Realistic IEEE 802.11 simulations using the ns-2 network simulator are provided to demonstrate the excellent performance of the proposed estimators     

Modulo-2piphase sequence estimation (Corresp.)

The probabilistic evolution of random walk on the circle is studied, and the results are used to derive a maximum {em a posteriori} probability (MAP) sequence estimator for phase. The sequence estimator is a Viterbi tracker for tracking phase on a finite-dimensional grid in[-pi,pi). The algorithm is shown to provide a convenient method for obtaining fixed-lag phase estimates. Performance characteristics are presented and compared with several published nonlinear filtering algorithms.     

A new adaptive equalizer with channel estimator for mobile radiocommunication

For unknown mobile radio channels with severe intersymbol interference (ISI), a maximum likelihood sequence estimator, such as a decision feedback equalizer (DFE) having both feedforward and feedback filters, needs to handle both precursors and postcursors. Consequently, such an equalizer is too complex to be practical. This paper presents a new reduced-state, soft decision feedback Viterbi equalizer (RSSDFVE) with a channel estimator and predictor. The RSSDFVE uses maximum likelihood sequence estimation (MLSE) to handle the precursors and truncates the overall postcursors with the soft decision of the MLSE to reduce the implementation complexity. A multiray fading channel model with a Doppler frequency shift is used in the simulation. For fast convergence, a channel estimator with fast start-up is proposed. The channel estimator obtains the sampled channel impulse response (CIR) from the training sequence and updates the RSSDFVE during the bursts in order to track changes of the fading channel. Simulation results show the RSSDFVE has nearly the same performance as the MLSE for time-invariant multipath fading channels and better performance than the DFE for time-variant multipath fading channels with less implementation complexity than the MLSE. The fast start-up (FS) channel estimator gives faster convergence than a Kalman channel estimator. The proposed RSSDFVE retains the MLSE structure to obtain good performance and only uses soft decisions to subtract the postcursor interference. It provides the best tradeoff between complexity and performance of any Viterbi equalizers     

An improvement to the interacting multiple model (IMM) algorithm

Computing the optimal conditional mean state estimate for a jump Markov linear system requires exponential complexity, and hence, practical filtering algorithms are necessarily suboptimal. In the target tracking literature, suboptimal multiple-model filtering algorithms, such as the interacting multiple model (IMM) method and generalized pseudo-Bayesian (GPB) schemes, are widely used for state estimation of such systems. We derive a reweighted interacting multiple model algorithm. Although the IMM algorithm is an approximation of the conditional mean state estimator, our algorithm is a recursive implementation of a maximum a posteriori (MAP) state sequence estimator. This MAP estimator is an instance of a previous version of the EM algorithm known as the alternating expectation conditional maximization (AECM) algorithm. Computer simulations indicate that the proposed reweighted IMM algorithm is a competitive alternative to the popular IMM algorithm and GPB methods     

Batch and Sequential Bayesian Estimators of the Number of Active Terminals in an IEEE 802.11 Network

The performance of the IEEE 802.11 protocol based on the distributed coordination function (DCF) has been shown to be dependent on the number of competing terminals and the backoff parameters. Better performance can be expected if the parameters are adapted to the number of active users. In this paper we develop both off-line and online Bayesian signal processing algorithms to estimate the number of competing terminals. The estimation is based on the observed use of the channel and the number of competing terminals is modeled as a Markov chain with unknown transition matrix. The off-line estimator makes use of the Gibbs sampler whereas the first online estimator is based on the sequential Monte Carlo (SMC) technique. A deterministic variant of the SMC estimator is then developed, which is simpler to implement and offers superior performance. Finally a novel approximate maximum a posteriori (MAP) algorithm for hidden Markov models (HMM) with unknown transition matrix is proposed. Realistic IEEE 802.11 simulations using the ns-2 network simulator are provided to demonstrate the excellent performance of the proposed estimators.      

噪声环境下遗传算法的收敛性和收敛速度估计

 问题求解的环境往往非常复杂,不确定的环境因素、人为因素等都可导致问题处于噪声环境,从而影响实际优化问题的目标函数值的评价.噪声环境下遗传算法的研究在国内外均起步较晚,特别是收敛性和收敛速度的分析是该领域急待解决的问题.本文根据优胜劣汰遗传算法的特性,基于吸收态Markov链的数学模型证明了噪声环境下优胜劣汰遗传算法的收敛性,提出了噪声环境下优胜劣汰遗传算法的首达最优解期望时间的估算方法.     

Simulated annealing for maximum a posteriori parameter estimationof hidden Markov models

Hidden Markov models are mixture models in which the populations from one observation to the next are selected according to an unobserved finite state-space Markov chain. Given a realization of the observation process, our aim is to estimate both the parameters of the Markov chain and of the mixture model in a Bayesian framework. We present an original simulated annealing algorithm which, in the same way as the EM (expectation-maximization) algorithm, relies on data augmentation, and is based on stochastic simulation of the hidden Markov chain. This algorithm is shown to converge toward the set of maximum a posteriori (MAP) parameters under suitable regularity conditions     

Bayesian decision feedback for segmentation of binary images

We present real-time algorithms for the segmentation of binary images modeled by Markov mesh random fields (MMRFs) and corrupted by independent noise. The goal is to find a recursive algorithm to compute the maximum a posteriori (MAP) estimate of each pixel of the scene using a fixed lookahead of D rows and D columns of the observations. First, this MAP fixed-lag estimation problem is set up and the corresponding optimal recursive (but computationally complex) estimator is derived. Then, both hard and soft (conditional) decision feedbacks are introduced at appropriate stages of the optimal estimator to reduce the complexity. The algorithm is applied to several synthetic and real images. The results demonstrate the viability of the algorithm both complexity-wise and performance-wise, and show its subjective relevance to the image segmentation problem.     

A multiscale random field model for Bayesian image segmentation

Many approaches to Bayesian image segmentation have used maximum a posteriori (MAP) estimation in conjunction with Markov random fields (MRF). Although this approach performs well, it has a number of disadvantages. In particular, exact MAP estimates cannot be computed, approximate MAP estimates are computationally expensive to compute, and unsupervised parameter estimation of the MRF is difficult. The authors propose a new approach to Bayesian image segmentation that directly addresses these problems. The new method replaces the MRF model with a novel multiscale random field (MSRF) and replaces the MAP estimator with a sequential MAP (SMAP) estimator derived from a novel estimation criteria. Together, the proposed estimator and model result in a segmentation algorithm that is not iterative and can be computed in time proportional to MN where M is the number of classes and N is the number of pixels. The also develop a computationally efficient method for unsupervised estimation of model parameters. Simulations on synthetic images indicate that the new algorithm performs better and requires much less computation than MAP estimation using simulated annealing. The algorithm is also found to improve classification accuracy when applied to the segmentation of multispectral remotely sensed images with ground truth data.     

基于马尔科夫链的灰狼优化算法收敛性研究

针对灰狼优化算法（Grey Wolf Optimization,GWO）在收敛性研究上的不足,首先,通过定义灰狼群状态转移序列,建立了GWO算法的马尔科夫（Markov）链模型,通过分析Markov链的性质,证明它是有限齐次 Markov链;其次,通过分析灰狼群状态序列最终转移状态,结合随机搜索算法的收敛准则,验证了GWO算法的全局收敛性;最后,对典型测试函数、偏移函数及旋转函数进行仿真实验,并与多种群体智能算法进行对比分析.实验结果表明,GWO算法具有全局收敛性强、计算耗时短和寻优精度高等优势.     

A matched nonlinearity for phase estimation of a PSK- modulated carrier (Corresp.)

A nonlinear phase estimator for a phase-shift keyed (PSK)-modulated carrier has been developed by Viterbi and Viterbi. Their analysis is extended, and an optimal or "matched" nonlinearity is derived for the estimator.     

Optimal sequence estimators for statistically unknown binary sources and channels (Corresp.)

We consider an information source that is an independent identically distributed (i.i.d.) binary sequence governed by unknown probability measures. The information sequence is transferred through a memoryless binary channel with unknown cross-over probabilities. The channel model also represents those cases in which an input quantizer is always used, so that the incoming information-bearing observations are threshold crossings of the observation process, and the unknown cross-over probabilities are associated with uncertainties concerning the signal-to-noise ratio (SNR). We derive and study the optimal (under a minimum error-probability criterion) sequence estimator (which utilizes the observed threshold crossings). The receiver is described by a practical implementable algorithm that involves a shortest path calculation, which is performed using the Viterbi algorithm, and appropriately incorporates the sufficient statistics of the unknown parameters. Its similarity to unsupervised decision-directed learning procedures is noted.     

Reduced-state sequence estimation of digital sequences indispersive channels using state partitioning

A reduced-state sequence estimator for linear dispersive channels is described. The estimator is based on partitioning the set of all possible channel states in a way that defines a trellis with fewer states, and thus reduces complexity. Such a set partitioning approach provides a good performance/complexity tradeoff. The new technique is a generalisation of that described by Duel-Hallen and Heegard [1989]. The Viterbi algorithm (VA) is used to search for the best path through the reduced state trellis