Maximum-likelihood reconstruction of transmission images in emission computed tomography via the EM algorithm

The expectation-maximization (EM) algorithm for computing maximum-likelihood estimates of transmission images in positron-emission tomography (PET) (see K. Lange and R. Carson, J. Comput. Assist. Tomogr., vol.8, no.2, p.306-16, 1984) is extended to include measurement error, accidental coincidences and Compton scatter. A method for accomplishing the maximization step using one step of Newton's method is proposed. The algorithm is regularized with the method of sieves. Evaluations using both Monte Carlo simulations and phantom studies on the Siemens 953B scanner suggest that the algorithm yields unbiased images with significantly lower variances than filtered-backprojection when the images are reconstructed to the intrinsic resolution. Large features in the images converge in under 200 iterations while the smallest features required up to 2,000 iterations. All but the smallest features in typical transmission scans converge in approximately 250 iterations. The initial implementation of the algorithm requires 50 sec per iteration on a DECStation 5000.     

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.     

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.     

DESIGN OF MICROSTRIP LANGE COUPLER BASED ON EM-ANN MODEL

Electromagnetically trained artificial neural network (EM-ANN) model for microstrip Lange Coupler is presented. Full-wave EM analysis software is employed to characterize the Lange Coupler. The EM-ANN model is then designed using physical parameters as inputs and S-parameters as outputs. Once the EM-ANN model is trained, it can be used to find the optimal physical structure of the Lange Coupler for a given application using optimization technique. A Ka-band microstrip Lange Coupler is designed by this method. The simulated results of the Lange Coupler show that the insert loss is better than ?3.64 dB; the amplitude balance is less than 0.55 dB and the phase balance is less than 0.52°from the 90°phase difference over the 30 to 40 GHz frequency range.     

A unified method for measurement and tracking of contacts from anarray of sensors

A multiple target track estimation method that operates directly from array data is presented. The maximum a-posteriori (MAP) estimator for contact states is derived for temporally uncorrelated signals and uncorrelated contact tracks, where the number of contacts is assumed known. This estimator is an iterative algorithm employing a nonlinear programming (NLP) penalty method in conjunction with an expectation-maximization (EM) algorithm. The NLP technique is used to find the MAP track estimate based on the synthetic signal estimates produced by the EM algorithm. This method eliminates the data association step of traditional multitarget tracking approaches by conditioning the measurement process on individual target state distributions. It results in a process similar to the EM algorithm for direction finding, with an additional penalty term imposed by the track distributions. The algorithm is derived as a batch method. An extension to support sequential tracking is also developed. Simulation results for a relevant submarine towed array scenario are presented and discussed     

基于EM算法的宽带信号DOA估计及盲分离

本文提出了一种基于EM算法的宽带信号DOA估计与盲分离方法.首先将宽带混合信号转换到频域,然后综合利用带宽内所有频点信息建立似然函数,在此基础上推导出宽带条件下的EM迭代式,从而实现宽带信号DOA及波形的联合估计.并且本文通过分析EM算法的收敛性,自适应的设定角度搜索空间,提高了算法的运算效率.与传统方法相比,本文方法运用的有效信息更多,因此,其在DOA估计精度及波形恢复性能方面都更有优势.仿真实验表明了该算法的有效性.     

Geometric derivation of expectation-maximization and generalized successive interference cancellation algorithms with applications to CDMA channel estimation

The expectation-maximization (EM) algorithm is well established as a computationally efficient method for separable signal parameter estimation. Here, a new geometric derivation and interpretation of the EM algorithm is given that facilitates the understanding of EM convergence properties. Geometric considerations lead to an alternative separable signal parameter estimator based on successive cancellation. The new generalized successive interference cancellation (GSIC) algorithm is then applied to multiuser delay and channel estimation for code-division multiple access (CDMA) radiolocation and communication. The radiolocation application uses a handshaking protocol in which multiple reference nodes transmit acknowledge (ACK) CDMA packets to a master node, which then computes round-trip travel times (RTTs). Simulation results comparing EM and GSIC are presented for the CDMA channel-estimation problem.     

Design of a 24-40 GHz balanced low noise amplifier using Lange couplers

A wide band(24-40 GHz)fully integrated balanced low noise amplifier(LNA)using Lange couplers was designed and fabricated with a 0.15/zm pseudomorphic HEMT(pHEMT)technology.A new method to design a low-loss and high-coupling Lange coupler for wide band application in microwave frequency was also presented.This Lange coupler has a minimum loss of 0.09 dB and a maximum loss of 0.2 dB over the bandwidth from 20 to 45 GHz.The measured results show that the realized four-stage balanced LNA using this Lange coupler exhibites a noise figure(NF)of less than 2.7 dB and the maximum gain of 30 dB;moreover,a noticeably improved reflection performance is achieved.The input VSWR and the output VSWR are respectively less than 1.45 and 1.35 dB across the 24-40 GHz frequency range.     

Identification of image and blur parameters in frequency domainusing the EM algorithm

We extend a method presented previously, which considers the problem of the semicausal autoregressive (AR) parameter identification for images degraded by observation noise only. We propose a new approach to identify both the causal and semicausal AR parameters and blur parameters without a priori knowledge of the observation noise power and the PSF of the degradation. We decompose the image into 1-D independent complex scalar subsystems resulting from the vector state-space model by using the unitary discrete Fourier transform (DFT). Then, by applying the expectation-maximization (EM) algorithm to each subsystem, we identify the AR model and blur parameters of the transformed image. The AR parameters of the original image are then identified by using the least squares (LS) method. The restored image is obtained as a byproduct of the EM algorithm.     

Hybrid Poisson/polynomial objective functions for tomographic imagereconstruction from transmission scans

This paper describes rapidly converging algorithms for computing attenuation maps from Poisson transmission measurements using penalized-likelihood objective functions. We demonstrate that an under-relaxed cyclic coordinate-ascent algorithm converges faster than the convex algorithm of Lange (see ibid., vol.4, no.10, p.1430-1438, 1995), which in turn converges faster than the expectation-maximization (EM) algorithm for transmission tomography. To further reduce computation, one could replace the log-likelihood objective with a quadratic approximation. However, we show with simulations and analysis that the quadratic objective function leads to biased estimates for low-count measurements. Therefore we introduce hybrid Poisson/polynomial objective functions that use the exact Poisson log-likelihood for detector measurements with low counts, but use computationally efficient quadratic or cubic approximations for the high-count detector measurements. We demonstrate that the hybrid objective functions reduce computation time without increasing estimation bias.     

A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography

The maximum likelihood (ML) expectation maximization (EM) approach in emission tomography has been very popular in medical imaging for several years. In spite of this, no satisfactory convergent modifications have been proposed for the regularized approach. Here, a modification of the EM algorithm is presented. The new method is a natural extension of the EM for maximizing likelihood with concave priors. Convergence proofs are given.     

A fast reconstruction algorthm for stationary positron emission tomography based on a modified em algorithm

An efficient iterative reconstruction method for positron emission tomography (PET) is presented. The algorithm is basically an enhanced EM (expectation maximization) algorithm with improved frequency response. High-frequency components of the ratio of measured to calculated projections are extracted and are taken into account for the iterative correction of image density in such a way that the correction is performed with a uniform efficiency over the image plane and with a flat frequency response. As a result, the convergence speed is not so sensitive to the image pattern or matrix size as the standard EM algorithm, and nonuniformity of the spatial resolution is significantly improved. Nonnegativity of the reconstructed image is preserved. Simulation studies have been made assuming two PET systems: a scanning PET with ideal sampling and a stationary PET with sparse sampling. In the latter, a "bank array" of detectors is employed to improve the sampling in the object plane. The new algorithm provides satisfactory images by two or three iterations starting from a flat image in either case. The behavior of convergence is monitored by evaluating the root mean square of C(b)-1 where C(b) is the correction factor for pixel b in the EM algorithm. The value decreases rapidly and monotonically with iteration number. Although the theory is not accurate enough to assure the stability of convergence, the algorithm is promising to achieve significant saving in computation compared to the standard EM algorithm.     

一种重建层状介质特性剖面的新方法

本文针对层状介质特性剖面的重建问题,研究了电磁波在层状介质中传播的时域数学模型;然后将层状介质特性剖面重建问题,归结为分布参数系统的参数辨识问题;并在前人工作的基础上,提出了一种新的重建层状介质特性剖面的有效方法。它优于通常的利用反射系数r(k)或脉冲响应来反演势函数V(z)的重建方法。此外本文在重建反演方面应用阶跃梯度分层反演法得出一种快速辨识算法,并给出了仿真实例。     

Wideband maximum likelihood direction finding and signal parameterestimation by using the tree-structured EM algorithm

The expectation maximization (EM) algorithm is presented for the case of estimating direction of arrivals of unknown deterministic wideband signals. Alternative regularized least squares estimation techniques for the required signal estimation and a tree structure for the data mapping in the EM algorithm are proposed. Extensive simulation results are presented for comparison of the proposed algorithms with the conventional EM approach and the current high-resolution methods of wideband direction finding     

基于核模糊C-均值和EM混合聚类算法的遥感图像分割

针对聚类算法在应用中分割速度慢、抑制噪声能力弱等问题,本文提出一种基于核模糊C-均值(Kernel Fuzzy Cmeans,KFCM)和融合期望最大化(EM)算法混合聚类的遥感图像分割。首先给原始KFCM算法引入隐含变量来对像素预定义类别,然后利用EM算法评价预定义的类别是否最优,以此完成对遥感图像的聚类分割。在利用EM算法进行评价时,对KFCM引入空间邻域信息,采用惯性权重对其初始化参数进行优化增强算法效率。与传统的聚类分割方法进行比较,研究结果表明,该方法速度快、效果好、精度也能满足应用要求,具有较高的应用价值。     

Causal and semicausal AR image model identification using the EMalgorithm

The method presented by T. Katayama and T. Hirai (1990), who considered the problem of semicausal autoregressive (AR) parameter identification for images degraded by observation noise, is extended. In particular, an approach to identifying both the causal and semicausal AR parameters without a priori knowledge of the observation noise power is proposed. The image is decomposed into 1-D independent complex scalar subsystems resulting from the vector state-space model, using the unitary discrete Fourier transform (DFT). Then the expectation-maximization algorithm is applied to each subsystem to identify the AR parameters of the transformed image. The AR parameters of the original image are then identified using the least-square method. The restored image is obtained as a byproduct of the EM algorithm.     

Accelerated iterative reconstruction for positron emission tomography based on the em algorithm for maximum likelihood estimation

The EM method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography (PET). The result is an iterative algorithm for image reconstruction that is finding increasing use in PET, due to its attractive theoretical and practical properties. Its major disadvantage is the large amount of computation that is often required, due to the algorithm's slow rate of convergence. This paper presents an accelerated form of the EM algorithm for PET in which the changes to the image, as calculated by the standard algorithm, are multiplied at each iteration by an overrelaxation parameter. The accelerated algorithm retains two of the important practical properties of the standard algorithm, namely the selfnormalization and nonnegativity of the reconstructed images. Experimental results are presented using measured data obtained from a hexagonal detector system for PET. The likelihood function and the norm of the data residual were monitored during the iterative process. According to both of these measures, the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm, for two different sets of data. Important theoretical properties remain to be investigated, namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator.     

Reliable prediction of EM radiation from a PCB at the design stageof electronic equipment

This paper presents a composite computer-aided design (CCAD) package for prediction of electromagnetic (EM) radiation from a printed circuit board (PCB) at the design stage of equipment. Such a CCAD package has been developed by combining an EM computation tool such as numerical electromagnetic code (NEC)-2, with other circuit design packages (CDPs). The method of prediction of EM radiation using the CCAD is well described in this paper. The predicted EM radiation has been validated experimentally and results showing good agreement are presented. Finally, the reliability of the CCAD package is investigated and presented     

用期望最大化算法抑制角闪烁的预处理方法

用高斯混合模型作为角闪烁噪声的近似统计模型,结合Kalman滤波器,提出了一种利用期望最大化(EM)算法抑制角闪烁噪声的预处理方法.首先采用EM算法处理一帧内的原始测量数据,预先得到目标真实位置的最大似然估计,这个预估计量服从渐进高斯分布,且其方差可求.然后将这个预估计量作为Kalman滤波器的输入量进行跟踪滤波,同时将目标位置的预测值作为下一帧EM迭代过程的初始值,进而形成闭环的跟踪滤波结构.仿真结果表明,该方法有效地抑制了角闪烁,使得Kalman滤波算法更加有效,从而提高了目标跟踪的精度.     

基于独立混合模型的EM算法参数初始化实现方法

隐马尔科夫树( Hidden Markov Tree, HMT )的状态不能被观测到,只能观测到另一个与状态有联系的量,通过观测量估计HMT模型参数是一个不完全数据参数估计问题。期望最大化( Expectation Maximization, EM )算法是一种求参数极大似然估计的迭代算法,可以用于解决不完全数据参数估计问题,因此被广泛应用于HMT模型的参数估计中。当初始参数偏离真实参数较大时,EM算法迭代次数多,收敛速度慢,通过一个计算量不大的参数初始化处理,能够有效减少EM算法的迭代次数,加快收敛速度。本文提出了一种基于独立混合模型的参数初始化方法,详细介绍了该方法的实现过程,通过采用独立混合模型进行参数初始化,使得EM算法的迭代次数明显减少,收敛速度大大提高。最后,计算机仿真验证了该方法的可行性和有效性。