Maximum likelihood reconstruction for emission tomography

Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density lambda = lambda(x, y, z) generates, and is to be reconstructed from, the number of counts n(*)(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate lambdainsertion mark of lambda which maximizes the probability p(n(*)|lambda) of observing the actual detector count data n(*) over all possible densities lambda. Let independent Poisson variables n(b) with unknown means lambda(b), b = 1, ..., B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ..., D with p(b,d) a one-step transition matrix, assumed known. We observe the total number n(*) = n(*)(d) of emissions in each detector unit d and want to estimate the unknown lambda = lambda(b), b = 1, ..., B. For each lambda, the observed data n(*) has probability or likelihood p(n(*)|lambda). The EM algorithm of mathematical statistics starts with an initial estimate lambda(0) and gives the following simple iterative procedure for obtaining a new estimate lambdainsertion mark(new), from an old estimate lambdainsertion mark(old), to obtain lambdainsertion mark(k), k = 1, 2, ..., lambdainsertion mark(new)(b)= lambdainsertion mark(old)(b)Sum of (n(*)p(b,d) from d=1 to D/Sum of lambdainsertion mark()old(b('))p(b('),d) from b(')=1 to B), b=1,...B.     

Maximum likelihood signal estimation for polarization sensitivearrays

The authors consider the problem of separating and estimating the waveforms of superimposed signals received by a polarization-sensitive array. Signal estimation is accomplished by a two-step maximum likelihood procedure: (i) The directions of arrival and polarization parameters of all the signals are estimated. (ii) The estimated signal is obtained as a linear combination of the array outputs, with weights which are computed from the estimated direction/polarization parameters. The objective of this study is to analyze the quality of the estimated signal in terms of the output signal-to-interference ratio (SIR) and output signal-to-noise ratio (SNR). Closed-form expressions are derived for the output SIR and SNR of a general diversely polarized array. By evaluating these expressions for selected test cases it is shown that polarization-sensitive arrays can provide significantly higher output SIR and SNR than uniformly polarized arrays. The performance improvement is especially significant for closed spaced sources with sufficiently different polarization characteristics     

Maximum likelihood estimation for a multivariate autoregressivemodel

The paper provides an analytical expression for the exact log likelihood function and its first derivatives for a multivariate autoregressive model. Based on these results, two algorithms for constructing the maximum likelihood estimate, using the Fisher's scoring technique, are proposed. The estimated model is guaranteed to be stable. Simulation examples show that this algorithm has good convergence properties and the resulting maximum likelihood estimator could perform better than earlier methods, in cases where the record length is short and the autoregressive polynomial has roots near the unit circle     

Maximum likelihood estimation for InSAR image co-registration

This paper presents a closed-form robust phase correlation based algorithm for performing image registration to subpixel accuracy. The subpixel translational shift information is directly ob- tained from the phase of the normalized cross power spectrum by using Maximum Likelihood Esti- mation （MLE）. The proposed algorithm also has slighter time complexity. Experimental results show that the proposed algorithm yields superior registration precision on the Cram@r-Rao Bound （CRB） in the presence of aliasing and noise.     

Maximum likelihood voting for fault-tolerant software with finiteoutput-space

When the output space of a multiversion software is finite, several software versions can give identical but incorrect outputs. This paper proposes a maximum likelihood voting (MLV) strategy for multiversion software with finite output-space under the assumption of failure independence. To estimate the correct result, MLV uses the reliability of each software version and determines the most likely correct result. In addition, two enhancements are made to MLV: (1) imposition of a requirement α* that the most likely correct output must have probability of at least α*; and (2) the voter can estimate when it has received one or more outputs from the software versions. If the probability that the estimated result is correct and is at least α*, then it immediately gives this estimated output. Since the voter need not wait for all the outputs before it can estimate, the required mean execution time can be reduced. The numerical results show that these MLV strategies have better performance than consensus voting and majority voting, especially when the variation of software version reliability is large. Enhancement #2 can appreciably reduce the mean execution time, especially when the software versions have larger execution time standard-deviation     

Maximum likelihood array processing for stochastic coherent sources

Maximum likelihood (ML) estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature. We focus on the equally relevant case of stochastic coherent signals. Explicit large-sample realizations are derived for the ML estimates of the noise power and the (singular) signal covariance matrix. The asymptotic properties of the estimates are examined, and some numerical examples are provided. In addition, we show the surprising fact that the ML estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ML estimates obtained by exploiting the coherent source information. Thus, the ML signal parameter estimator derived for the noncoherent case (or its large-sample realizations) asymptotically achieves the lowest possible estimation error variance (corresponding to the coherent Cramer-Rao bound)     

MIMO-OFDM系统信道最大似然估计研究

在深入分析MIMO-OFDM系统信道模型的基础上,提出了一种新的导频符号设计方案和采用最大似然比估计算法估计MIMO-OFDM信道,并分析了该算法的性能;计算机仿真结果表明在信道统计特性未知的条件下,采用所提出的导频符号设计方案效率高,估计性能优于RRE和LE等其他方法.     

Maximum likelihood angle estimation for signals with knownwaveforms

Maximum-likelihood estimation (MLE) of the arrival angles of narrowband plane waves when one or all signals have known waveforms is considered. Computationally efficient and rapidly converging algorithms that iteratively maximize the likelihood functions are presented. Cramer-Rao bounds for these estimators are obtained. The conditions under which incorporating knowledge of one or all of the signal waveforms in the estimators improves the accuracy of the angle estimates are described     

Maximum likelihood based framework for second-level adaptive prediction

A study is presented of a maximum likelihood based framework for second-level adaptive prediction which is formed from a group of predictors. It is a natural extension to first-level prediction which is formed directly from a group of pixels. The proposed framework offers a greater degree of freedom for adaptation and tackles the problem of model uncertainty that is inherent in first-level prediction methods. It is shown that the proposed methods of taking the weighted average and the weighted median of a group of predictions are alternative and competitive adaptive image prediction methods. The authors also present an extensive discussion on some related research works and theories, generalisation of proposed methods and some possible ways for further improvement.     

An exact maximum likelihood registration algorithm for data fusion

Data fusion is a process dealing with the association, correlation, and combination of data and information from multiple sources to achieve refined position and identity estimates. We consider the registration problem, which is a prerequisite process of a data fusion system to accurately estimate and correct systematic errors. An exact maximum likelihood (EML) algorithm for registration is presented. The algorithm is implemented using a recursive two-step optimization that involves a modified Gauss-Newton procedure to ensure fast convergence. Statistical performance of the algorithm is also investigated, including its consistency and efficiency discussions. In particular, the explicit formulas for both the asymptotic covariance and the Cramer-Rao bound (CRB) are derived. Finally, simulated and real-life multiple radar data are used to evaluate the performance of the proposed algorithm     

Maximum likelihood carrier phase recovery for coherently orthogonalCPFSK signals

ML estimation of carrier phase for coherently orthogonal continuous-phase frequency-shift-keying (COCPFSK) signals is considered. Although the estimator, in general is nonimplementable, its high and low signal-to-noise-ratio approximations both lead to linear readily implementable receiver structures. The high SNR approximation yields a DA receiver, whereas the low SNR approximation yields an NDA receiver. The performance of both receivers in term of bit error probability is analyzed. The existence of an unmodulated component in the sufficient statistical representation of a COCPFSK signal is pointed out, and it is shown how this component enters directly into maximum-like carrier recovery. This leads to interpretation of the NDA receiver as a generalization of the conventional matched-filter envelope-detector receiver. The insights gained here are useful to the problem of ML carrier recovery for Viterbi decoding of continuous phase modulation signals     

Maximum likelihood estimation for array processing in colored noise

Direction of arrival estimation of multiple sources, using a uniform linear array, in noise with unknown covariance is considered. The noise is modeled as a spatial autoregressive process with unknown parameters. Both stochastic and deterministic signal models are considered. For the random signal case, an approximate maximum likelihood estimator of the signal and noise parameters is derived. It requires numerical maximization of a compressed likelihood function over the unknown arrival angles. Analytical expressions for the MLEs of the signal covariance and the AR parameters are given. Similar results for the case of deterministic signals are also presented     

Maximum likelihood array processing for the estimation ofsuperimposed signals

An efficient algorithm for computing the maximum-likelihood estimates of multiple signals observed by an array of sensors is presented. The algorithm provides estimates of parameters related to the directional patterns of the sources as well as estimates of the location parameters of the sources. Furthermore, the algorithm is equally applicable to wideband sources and narrowband sources and does not require a knowledge of the statistical properties of the signals     

Maximum likelihood estimation for multivariate observations of Markov sources

Parameter estimation for multivariate functions of Markov chains, a class of versatile statistical models for vector random processes, is discussed. The model regards an ordered sequence of vectors as noisy multivariate observations of a Markov chain. Mixture distributions are a special case. The foundations of the theory presented here were established by Baum, Petrie, Soules, and Weiss. A powerful representation theorem by Fan is employed to generalize the analysis of Baum, {em et al.} to a larger class of distributions.     

Deterministic Maximum likelihood Approach for Localization of Near-field Sources

In this paper we proposed deterministic maximum likelihood approach for estimating the direction of arrival and range parameters of the near-field sources. Direct maximum likelihood estimation of near-field source parameters results in complicated multi-parameter optimization problems, we therefore reformulated the estimation problem in terms of actual-datasample, called the incomplete data and a hypothetical dataset, called the complete data and then devised the Expectation/Maximization iterative method for obtaining maximum likelihood estimates. The Expectation/Maximization algorithm decomposes the observed data into its components and then estimates the parameters of each signal component separately providing computationally efficient solution to the resulting optimization problem. The applicability and effectiveness of the proposed algorithm is illustrated by some numerical simulations.     

Maximum likelihood estimation of K distribution parameters for SARdata

The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the K distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. The present authors apply a maximum likelihood estimation method directly to the K distribution. They consider the situation for single-look SAR data as well as a simplified model for multilook data. They investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. They also compare their results with those from a new method given by Raghavan (1991) and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, they compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. They find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non-Rayleigh. They note that the distributions for the data set differ too little between ice types to allow discrimination based on differing distribution parameters     

Maximum likelihood estimation for long-range target tracking usingpassive sonar measurements

A Newton-type method is used to solve the target motion analysis (TMA) problem with respect to bearing and frequency measurements from a passive sonar system. In many long-range sonar situations the TMA problem is ill conditioned and suffers from a small signal-to-noise ratio. Although Kalman filters have been investigated extensively it is known that maximum likelihood (ML) estimation is superior in these cases. The main reason for the good performance of the ML method is that the underlying numerical optimization problem deals with the ill conditioning of the problem. This work illustrates how the conditioning depends on the geometry of the tracks and the signal-to-noise ratio. Monte Carlo simulations with respect to the measurement noise show the influence on the ML estimation performance for three specific cases concerning multileg situations and bottom bounce measurements     

Maximum likelihood estimation for failure analysis [IC yield]

This paper presents an iterative maximum likelihood (ML) estimation method for statistical analysis of yield loss. By means of inductive fault analysis (IFA) and circuit simulation, the mapping between defect types to the corresponding fault signature is constructed. Using the count of each fault signature occurrence, which is provided by a tester on defective ICs, the most likely causes of low yield are identified automatically without the need for physically deprocessing the defective IC's. We present an experiment on an SRAM cell array to illustrate the effectiveness of the iterative ML algorithm     

Maximum likelihood filters in spectral estimation problems

This paper begins with a classification of power spectral estimates from the point of view of bank filter analysis. To reinforce the interest of such a classification, a review of the main and most familiar procedures for spectral estimation is included. Starting from the most general approach, due to Frost, we indicate why it is not appropriate to classify Capon's maximum likelihood method as a low resolution procedure.The second part of the paper deals with a modification of the so-called maximum likelihood estimate in order to obtain the resolution which corresponds to a power density estimate. The modification provided here consists in a bandwidth normalization. The resulting estimate shows how the area of application of ML filters (as the data depending filters reported some years ago by Capon and Lacoss could be named) is considerably extended to a reliable procedure for power level and power density level estimation.We also explain in this paper how to get cross-spectral estimates from ML filters. From our point of view, this approach is the only one, among currently reported methods, that enhances the adequate levels of quality in order to compete with classical Fourier analyzers.In addition, the interesting ideas of Pisarenko about power function estimates can also be applied to the new approach presented here. The resulting family of power function estimates can further improve resolution up to the quality provided by SVD like methods, but avoiding the computational burden associated with them.     

Maximum likelihood analysis of cardiac late potentials

This study presents a new time-domain method for the detection of late potentials in individual leads. Basic statistical properties of the ECG samples are modeled in order to estimate the amplitude and duration of late potentials. The signal model accounts for correlation in both time and across the ensemble of beats. Late potentials are modeled as a colored process with unknown amplitude which is disturbed by white, Gaussian noise. Maximum likelihood estimation is applied to the model for estimating the amplitude of the late potentials. The resulting estimator consists of an eigenvector-based filter followed by a nonlinear operation. The performance of the maximum likelihood procedure was compared to that obtained by traditional time-domain analysis based on the vector magnitude. It was found that the new technique yielded a substantial improvement of the signal-to-noise ratio in the function used for endpoint determination. This improvement leads to a prolongation of the filtered QRS duration in cases with late potentials