Region tracking for non-rigid video objects in a non-parametric MAP framework

This paper presents a non-parametric maximum a posteriori MAP framework for tracking non-rigid video objects. We formulate the region tracking problem as a MAP probability problem and define the probabilistic models in terms of the distances between the intensity distribution of the object and that of its spatial- and temporal-neighborhood. Furthermore, in order to better model the complex intensity changes due to non-rigid movement, we propose to use a non-parametric method to approximate the likelihood and prior terms in the MAP problem. The proposed non-parametric estimation algorithm mostly relies on intensity features and requires no time-consuming motion estimation. Finally, we employ a contour evolution method in the MAP optimization step to iteratively track the object contour. The experimental results demonstrate that the proposed method achieves satisfactory results and outperforms the previous parametric method.     

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     

Performance analysis on an MAP fine timing algorithm in UWB multiband OFDM

In this paper we develop a fine synchronization algorithm for multiband OFDM transmission in the presence of frequency selective channels. This algorithm is based on maximum a posteriori (MAP) joint timing and channel estimation that incorporates channel statistical information, leading to considerable performance enhancement relative to existing maximum likelihood (ML) approaches. We carry out a thorough performance analysis of the fine timing algorithm, and link the diversity concept widely used in data communications to the timing performance. We show that the probability of the timing offset equal to or larger than Delta taps has a diversity order of N_B min(Delta, L) in Rayleigh fading channels, where N_B is the number of subbands and L is the number of channel taps. This result reveals that the timing estimate is very much concentrated around the true timing as the signal to noise ratio (SNR) increases. Our simulations confirm the theoretical analysis, and also demonstrate the robustness of the proposed timing algorithm against model mismatches in a realistic UWB indoor channel.     

EM算法在杂波环境下机动目标跟踪中的应用研究

EM(Expectation-Maximization)作为一种迭代求解非完备数据条件下极大似然(后验)参数估计问题的方法,在目标跟踪领域主要应用于被动跟踪及实时性要求不高的目标环境.该文推广了L.A.Johnston的理论成果,推导得出了一种基于AECM(Alternative Expectation ConditionMaximization)方法的杂波环境下实时机动目标跟踪箅法,算法中后验模型概率与关联概率由隐马尔科夫模型滤波计算得到.仿真计算表明,所提算法跟踪精度与IMM-PDA性能相当,算法是有效的.     

平衰落信道下ML和MAP信道估计与导频符号长度的关系性能比较

信道估计是无线通信系统必须加以解决的关键技术之一，采用导频符号辅助的方法进行信道估计是目前各类无线通信系统常用的方法。本文针对平衰落信道提出了最大似然(ML)算法和最大后验概率(MAP)估计算法，给出了ML估计和MAP估计之间的关系，仿真了MAP估计和ML估计的方差与导频符号长度的关系，提出当导频符号长度的取值超过20个符号长度时，MAP信道估计明显优于ML信道估计。     

Performance of nonlinear detectors in spatial multiplexing for spatially correlated channels

Spatial multiplexing is used in multiple input multiple output (MIMO) wireless systems to increase the data rate. Some nonlinear detectors, such as minimum mean square error (MMSE) Vertical Bell laboratories layered space-time (VBLAST), Maximum A-Posteriori (MMSE VBLAST MAP), and MMSE Improved VBLAST detectors are used in place of a over more complex detector, such as maximum likelihood detector or singular value decomposition based detector. We have presented simulation results of MIMO symbol error rate versus average SNR for MMSE VBLAST MAP and MMSE Improved VBLAST schemes assuming spatially correlated channels for M-ary QAM. We have observed that the performance of MMSE VBLAST MAP and MMSE Improved VBLAST detectors is almost identical in spatially uncorrelated channels. However, in the case of spatially correlated channels, MMSE Improved VBLAST outperforms MMSE VBLAST MAP. We have also seen that complexity of the Improved VBLAST algorithm is higher than the complexity of VBLAST MAP algorithm.     

Modification of the MAP algorithm for memory savings

It is usually assumed that all state metric values are necessary in the maximum a posteriori (MAP) algorithm in order to compute the a posteriori probability (APP) values. This work extends the mathematical derivation of the original MAP algorithm and shows that the log likelihood values can be computed using only partial state metric values. By processing N stages in a trellis concurrently, the proposed algorithm results in savings in the required memory size and leads to a power efficient implementation of the MAP algorithm in channel decoding. The computational complexity analysis for the proposed algorithm is presented. Especially for the N=2 case, we show that the proposed algorithm halves the memory requirement without increasing the computational complexity.     

Likelihood maximization for list-mode emission tomographic imagereconstruction

The maximum a posteriori (MAP) Bayesian iterative algorithm using priors that are gamma distributed, due to Lange, Bahn and Little, is extended to include parameter choices that fall outside the gamma distribution model. Special cases of the resulting iterative method include the expectation maximization maximum likelihood (EMML) method based on the Poisson model in emission tomography, as well as algorithms obtained by Parra and Barrett and by Huesman et al. that converge to maximum likelihood and maximum conditional likelihood estimates of radionuclide intensities for list-mode emission tomography. The approach taken here is optimization-theoretic and does not rely on the usual expectation maximization (EM) formalism. Block-iterative variants of the algorithms are presented. A self-contained, elementary proof of convergence of the algorithm is included.     

Fast maximum entropy approximation in SPECT using the RBI-MAP algorithm

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.     

Fast EM-like methods for maximum "a posteriori" estimates in emission tomography

The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission computed tomography that became very popular for solving the ML problem because of its attractive theoretical and practical properties. Recently, (Browne and DePierro, 1996 and Hudson and Larkin, 1994) block sequential versions of the EM algorithm that take advantage of the scanner's geometry have been proposed in order to accelerate its convergence. In Hudson and Larkin, 1994, the ordered subsets EM (OS-EM) method was applied to the ML problem and a modification (OS-GP) to the maximum a posteriori (MAP) regularized approach without showing convergence. In Browne and DePierro, 1996, we presented a relaxed version of OS-EM (RAMLA) that converges to an ML solution. In this paper, we present an extension of RAMLA for MAP reconstruction. We show that, if the sequence generated by this method converges, then it must converge to the true MAP solution. Experimental evidence of this convergence is also shown. To illustrate this behavior we apply the algorithm to positron emission tomography simulated data comparing its performance to OS-GP.     

Efficient Huber-Markov edge-preserving image restoration.

The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.     

Convergence of the maximum a posteriori path estimator in hiddenMarkov models

In a hidden Markov model (HMM) the underlying finite-state Markov chain cannot be observed directly but only by an additional process. We are interested in estimating the unknown path of the Markov chain. The most widely used estimator is the maximum a posteriori path estimator (MAP path estimator). It can be calculated effectively by the Viterbi (1967) algorithm as is, e.g., frequently done in the field of coding theory, correction of intersymbol interference, and speech recognition. We investigate (component-wise) convergence of the MAP path estimator. Convergence is shown under the condition of unbounded likelihood ratios. This condition is satisfied in the important case of HMMs with additive white Gaussian noise. We also prove convergence, if the Markov chain has two states. The so-called Viterbi paths are an important tool for obtaining these results     

Image reconstruction by conditional entropy maximisation for PET system

The authors show that the conditional entropy maximisation algorithm is a generalised version of the maximum likelihood algorithm for positron emission tomography (PET). Promising properties of the conditional entropy maximisation algorithm are as follows: an assumption is made that the entropy of the information content of the data should be maximised; it is a consistent way of selecting an image from the very many images that fit the measurement data; this approach takes care of the positivity of the reconstructed image pixels, since entropy does not exist for negative image pixel values; and inclusion of prior distribution knowledge in the reconstruction process is possible. Simulated experiments performed on a PET system have shown that the quality of the reconstructed image using the entropy maximisation method is good. A Gibbs distribution is used to incorporate prior knowledge into the reconstruction process. The mean squared error (MSE) of the reconstructed images shows a sharp new dip, confirming improved image reconstruction. The entropy maximisation method is an alternative approach to maximum likelihood (ML) and maximum a posteriori (MAP) methodologies.     

CPM调制的迭代检测技术

CPM信号具有包络恒定、峰均比小、功率利用率高的优点。针对CPM信号的特征,比较了最大似然序列检测Viterbi算法和逐符号的最大后验概率(MAP)解调算法的特点,重点研究了使用迭代检测技术进行软输入输出解调及译码的MAP解调方法。在AWGN信道条件下对CPM全响应和部分响应信号进行了误码性能仿真,结果表明采用相干解调和译码,迭代检测方案可得到较高的编码增益。     

A statistical multiscale framework for Poisson inverse problems

This paper describes a statistical multiscale modeling and analysis framework for linear inverse problems involving Poisson data. The framework itself is founded upon a multiscale analysis associated with recursive partitioning of the underlying intensity, a corresponding multiscale factorization of the likelihood (induced by this analysis), and a choice of prior probability distribution made to match this factorization by modeling the “splits” in the underlying partition. The class of priors used here has the interesting feature that the “noninformative” member yields the traditional maximum-likelihood solution; other choices are made to reflect prior belief as to the smoothness of the unknown intensity. Adopting the expectation-maximization (EM) algorithm for use in computing the maximum a posteriori (MAP) estimate corresponding to our model, we find that our model permits remarkably simple, closed-form expressions for the EM update equations. The behavior of our EM algorithm is examined, and it is shown that convergence to the global MAP estimate can be guaranteed. Applications in emission computed tomography and astronomical energy spectral analysis demonstrate the potential of the new approach     

An empirical Bayes estimator for in-scale adaptive filtering

A scale-adaptive filtering scheme is developed for underspread channels based on a model of the linear time-varying channel operator as a process in scale. Recursions serve the purpose of adding detail to the filter estimate until a suitable measure of fidelity and complexity is met. Resolution of the channel impulse response associated with its coherence time is naturally modeled over the observation time via a Gaussian mixture assignment on wavelet coefficients. Maximum likelihood, approximate maximum a posteriori (MAP) and posterior mean estimators, as well as associated variances, are derived. Doppler spread estimation associated with the coherence time of the filter is synonymous with model order selection and a MAP estimate is presented and compared with Laplace's approximation and the popular AIC. The algorithm is implemented with conjugate-gradient iterations at each scale, and as the coherence time is recursively decreased, the lower scale estimate serves as a starting point for successive reduced-coherence time estimates. The algorithm is applied to a set of simulated sparse multipath Doppler spread channels, demonstrating the superior MSE performance of the posterior mean filter estimator and the superiority of the MAP Doppler spread stopping rule.     

Terra MODIS第5波段红外遥感影像条带噪声的探测与校正

由于Terra MODIS传感器第5波段（1.230~1.250 m）中部分探测元件出现故障,从而导致整幅影像上存在明显的条带噪声。对于地理校正后的MODIS影像数据,其条带噪声的分布并不是完全规则的,还可能存在不连续的现象,加大了对噪声进行处理的难度。提出一种对条带噪声进行检测与去除的方法,首先利用局部梯度对条带噪声的位置进行探测。然后在基于最大后验概率的框架下结合噪声模型与Huber-Markov先验,并通过梯度下降算法进行噪声的去除。使用真实的遥感数据进行了实验,所展示的恢复后数据和对应的频谱图都证明了文中方法的有效性。     

Estimation of images and nonrigid deformations in gated emission CT

In this paper, we propose and test a new iterative algorithm to simultaneously estimate the nonrigid motion vector fields and the emission images for a complete cardiac cycle in gated cardiac emission tomography. We model the myocardium as an elastic material whose motion does not generate large amounts of strain. As a result, our method is based on minimizing an objective function consisting of the negative logarithm of a maximum likelihood image reconstruction term, the standard biomechanical model of strain energy, and an image matching term that ensures a measure of agreement of intensities between frames. Simulations are obtained using data for the four-dimensional (4-D) NCAT phantom. The data models realistic noise levels in a typical gated myocardial perfusion SPECT study. We show that our simultaneous algorithm produces images with improved spatial resolution characteristics and noise properties compared with those obtained from postsmoothed 4-D maximum likelihood methods. The simulations also demonstrate improved motion estimates over motion estimation using independently reconstructed images.     

Bayesian kernel methods for analysis of functional neuroimages

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.     

Performance evaluation of list sequence MAP decoding

List-sequence (LS) decoding has the potential to yield significant coding gain additional to that of conventional single-sequence decoding, and it can be implemented with full backward compatibility in systems where an error-detecting code is concatenated with an error-correcting code. LS maximum-likelihood (ML) decoding provides a list of estimated sequences in likelihood order. For convolutional codes, this list can be obtained with the serial list Viterbi algorithm (SLVA). Through modification of the metric increments of the SLVA, an LS maximum a posteriori (MAP) probability decoding algorithm is obtained that takes into account bitwise a priori probabilities and produces an ordered list of sequence MAP estimates. The performance of the resulting LS-MAP decoding algorithm is studied in this paper. Computer simulations and approximate analytical expressions, based on geometrical considerations of the decision domains of LS decoders, are presented. We focus on the frame-error performance of LS-MAP decoding, with genie-assisted error detection, on the additive white Gaussian noise channel. It is concluded that LS-MAP decoding exploits a priori information more efficiently, in order to achieve performance improvements, than does conventional single-sequence MAP decoding. Interestingly, LS-MAP decoding can provide significant improvements at low signal-to-noise ratios, compared with LS-ML decoding. In this environment, it is furthermore observed that feedback convolutional codes offer performance improvements over their feedforward counterparts. Since LS-MAP decoding can be implemented in existing systems at a modest complexity increase, it should have a wide area of applications, such as joint source-channel decoding and other kinds of iterative decoding.