A multigrid expectation maximization reconstruction algorithm for positron emission tomography

The problem of reconstruction in positron emission tomography (PET) is basically estimating the number of photon pairs emitted from the source. Using the concept of the maximum-likelihood (ML) algorithm, the problem of reconstruction is reduced to determining an estimate of the emitter density that maximizes the probability of observing the actual detector count data over all possible emitter density distributions. A solution using this type of expectation maximization (EM) algorithm with a fixed grid size is severely handicapped by the slow convergence rate, the large computation time, and the nonuniform correction efficiency of each iteration, which makes the algorithm very sensitive to the image pattern. An efficient knowledge-based multigrid reconstruction algorithm based on the ML approach is presented to overcome these problems.     

Fourier correction for spatially variant collimator blurring in SPECT

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.     

Approximations to a Joint Detection/Decoding Algorithm

The problem of optimally detecting coded data transmitted over channels which produce intersymbol interference is examined. The optimum bit-by-bit detector structure which directly estimates the transmitted data symbols from the received signal at the channel output is given. The performance of this joint detector is contrasted to that of a receiver in which the decision process is partitioned into the usual detector followed by a decoder. Even when the detector and decoder are separately optimized (bit-by-bit criterion), the joint detector is shown to considerably out perform the separately optimized structure, thereby illustrating the considerable loss of information resulting from partitioning of the decision process. Two near optimum algorithms which significantly reduce the complexity of the optimum joint detector are given. These relatively simple algorithms, which approximate the joint detector, are shown to be capable of performance superior to that of the more complex, separately optimized detector/decoder structure. The joint detector and the approximate algorithms presented offer an attractive alternative to the soft decision decoder which also attempts to overcome the loss of information resulting from sharp partitioning of the detector/ decoder decisions.     

Adaptive detection of signals with linear feature mappings andrepresentations

In a previous paper, Reed (1993) developed a new test function for detecting a 2-D signal with limited prior information about the signal waveform and the statistical properties of clutter. This was accomplished by substituting a maximum likelihood estimate (MLE) of the unknown clutter covariance matrix and the MLE's of the amplitudes of the selected signal-feature components into a maximum invariant ratio test. However, performance analyses of this detector were not obtained. In this paper, the test statistic in Reed's previous paper is extended to the complex domain for application to synthetic aperture radar (SAR) imagery. The performance of the detector is studied analytically. Closed-form expressions for the performance of the detector, under both hypotheses H₀ and H₁ are obtained. The theoretical results show that the detectability of the test is strongly effected by the feature mapping and selection techniques used to represent a signal. Here the effectiveness of a feature representation is evaluated in terms of the number of features needed to represent a signal and the separability of those features from the clutter background. The dependence of the detection probability on the effectiveness of the features is quantitatively shown by a set of performance curves. The resulting analyses indicate that the detector has the property of a constant false alarm rate (CFAR). To make the results of the detection performance analysis more applicable to real problems, the loss due to a “mismatched feature” representation is also studied analytically     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

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.     

The mutual information criterion for SPECT aperture evaluation and design

An aperture performance criterion for single-photon-emission computed tomography (SPECT) that is based on the mutual information (MI) between the source and detector processes is proposed. The MI is a measure of the reduction in uncertainty of the emitter location, given the detector data, and it takes account of the inherent tradeoffs between the effects of sensitivity and resolution on source estimation accuracy. Specific expressions for the MI are derived for one-dimensional linear geometries and two-dimensional, parallel-slice, ring geometries under the assumptions of Poisson emission times, uniform emission angles, no scattering, and a known lost-count correction factor. For one-dimensional geometries a necessary and sufficient condition for an aperture to maximize the mutual information is given. The MI-optimal apertures are derived for various source distributions using an iterative maximization procedure. The MI is then numerically calculated for various ring apertures associated with the parallel-slice SPRINT II system.     

Light Emission to Time Resolved Emission For IC Debug and Failure Analysis

Light emission is routinely used to locate abnormal areas in failed ICs. Localization is done while the device is activated by a test pattern in a loop. Time Resolved Emission (TRE) has the potential to analyse faults by studying the emission of one area as a function of time. For failure analysis both techniques are valuable to identify where and when abnormal emission events have occurred. At low VDD, using only one or the other emission technique has shown some limitations. A solution, presented here, is to add a NIR PMT detector on an existing light emission microscope. Choice of detectors, performances and implementation are detailed on 120 and 90 nm structures.     

On Optimal Detection of Band-Limited PAM Signals with Excess Bandwidth

PAM data transmission receivers accomplishing maximum likelihood sequence detection (MLSD) usually require a matched filter prefilter, a sampler at the symbol rate, and a Viterbi algorithm detector. When the channel is unknown or slowly changing, one must use an adaptive matched filter prefilter. We examine an alternative optimum receiver whose optimality is independent of the matched filter prefilter and which is applicable when the channel is effectively band-limited. The sampler in the proposed receiver operates at a rate faster than the data symbol rate, enabling one to replace the matched filter by a fixed low-pass filter and still ensure that the maximum likelihood detector is supplied with a set of sufficient statistics. It is shown that the matched filter is incorporated within a modified Viterbi detector without increasing the number of states in the algorithm, although the Viterbi detector must perform computations at approximately twice the usual rate. Simulations support the optimality of the new receiver and quantitatively indicate the degradation in performance experienced by some adaptive receivers previously proposed.     

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.     

On the quantum limit of laser amplifier detectors

The quantum limit of a laser amplifier used as a detector is calculated. It is shown that the amplified output can be quantum correlated to the detector readout. However, as an information tap, the amplifying detector is no better than a lossless linear beamsplitter due to the added spontaneous emission noise     

Numerical study on performance of pyramidal and conical isotropic etched single emitters

A full three-dimensional model was implemented in order to investigate the electrical characteristics of conical and pyramidal isotropic etched emitters. The analysis was performed using the finite element method (FEM). The simulations of both emitters were modeled using a combination of tetrahedral and hexahedral elements that are capable of creating a mapped and regular mesh in the vacuum region and an irregular mesh near the surfaces of the emitter. The electric field strengths and electric potentials are computed and can be used to estimate the field enhancement factor as well as the current density using the Fowler-Nordheim (FN) theory. The FEM provides results at nodes located at discrete coordinates in space; therefore, the surface of the emitter can be generated through a function interpolating a set of scattered data points. The emission current is calculated through integration of the current density over the emitter tip surface. The influences of the device geometrical structure on its potential distribution, electric field and emission characteristics are discussed.     

Adaptive Detection and Interference Rejection of Multiple Point-Like Radar Targets

We present an adaptive algorithm aimed at detecting multiple point-like radar targets embedded in correlated Gaussian noise. The proposed detector modifies and improves the adaptive beamformer orthogonal rejection test (ABORT) idea to address detection of multiple targets. More precisely, it relies on the so-called two-step generalized likelihood ratio test (GLRT) design procedure implemented without assignment of a distinct set of secondary data. The newly proposed detector can guarantee the constant false alarm rate (CFAR) property and the performance assessment, conducted resorting to simulated data, has shown that it exhibits better rejection capabilities of mismatched signals than previously proposed detectors, at the price of an acceptable performance loss for matched signals     

Multiuser macrodiversity detection in asynchronous DS-CDMA systems

The authors present a performance analysis for the reverse link of a wireless DS-code division multiple access (CDMA) system that exploits macrodiversity reception while adopting the maximum likelihood (ML) multiuser detector for the basic detection. This appears to be the first analytical treatment of the ML multiuser macrodiversity detector in asynchronous DS-CDMA systems. They also include the effects of frequency selective fading, imperfect synchronization, and imperfect channel state information. Power control and connection control companion algorithms are presented to assess the value of this detector in a system context. The authors have shown that the ML multiuser-macrodiversity detector is capable of reducing the bit-error rate for many users by several orders of magnitude compared with multiuser detectors that operate on each antenna separately.     

List-mode maximum-likelihood reconstruction applied to positron emission mammography (PEM) with irregular sampling

We present a preliminary study of list-mode likelihood reconstruction of images for a rectangular positron emission tomograph (PET) specifically designed to image the human breast. The prospective device consists of small arrays of scintillation crystals for which depth of interaction is estimated. Except in very rare instances, the number of annihilation events detected is expected to be far less than the number of distinguishable events. If one were to histogram the acquired data, most histogram bins would remain vacant. Therefore, it seems natural to investigate the efficacy of processing events one at a time rather than processing the data in histogram format. From a reconstruction perspective, the new tomograph presents a challenge in that the rectangular geometry leads to irregular radial and angular sampling, and the field of view extends completely to the detector faces. Simulations are presented that indicate that the proposed tomograph can detect 8-mm-diameter spherical tumors with a tumor-to-background tracer density ratio of 3:1 using realistic image acquisition parameters. Spherical tumors of 4-mm diameter are near the limit of detectability with the image acquisition parameters used. Expressions are presented to estimate the loss of image contrast due to Compton scattering.     

Modeling and algorithm development for automated optical endpointing of an HBT emitter etch

This paper discusses the development of a high-accuracy endpointing algorithm for the emitter etch of a heterojunction bipolar transistor (HBT). Fabrication of high-performance HBTs using self-aligned base-emitter processes requires etching through the emitter layer and stopping with very high accuracy on the base layer. The lack of selectivity in dry etching coupled with the high etch rates possible in high density plasmas render the use of a standard timed overetch impractical, especially as device layers continue to become thinner. The etch process under study requires the complete removal of an AlInAs emitter while etching no more than 5 nm of the underlying GaInAs base layer. Etch products are monitored using optical emission spectroscopy (OES) to determine etch endpoint. The process under study relies on the intensity of the 417.2 nm Ga emission line. The detection of the Ga line indicates that the etch has reached the GaInAs layer. However, the presence of a time-varying Ga baseline signal before endpoint and significant noise in the OES signal necessitate more than a simple threshold scheme for critical endpoint detection. The algorithm presented here is based on a generalized likelihood ratio with a signature function. This algorithm is robust to variance in the optical gains of the measurement equipment and is applicable to other etch processes. Experimental results of automated endpointing using this algorithm are presented in the form of pre- and post-etch ex situ film thickness measurements.     

Field Emission of Electrons Powered by a Triboelectric Nanogenerator

Field emission of electrons usually requires high voltage (HV) of at least 100 V, which limits its applications due to the high cost, instability, portability issues, etc., of the HV instrument. Triboelectric nanogenerators (TENGs) have been developed to provide an HV of at least several kV for portable/mobile instrument, with controllability already demonstrated. Here, the field emission of electrons driven by TENG, namely, tribo‐field emission, is presented for the first time. The emission voltage and the charge transfer per cycle can be tuned and controlled by TENG. The current peak generated from TENG with limited charge transfer is demonstrated to be more favorable than the direct current HV source in terms of emitter protection. A unidirectional continuous emission current is achieved through the tribo‐field emission. A cathode‐ray tube can be powered by TENG, with hours of illumination demonstrated through only one sliding motion. Such approach can provide a potential solution for controllable, stable, and portable field‐emission devices without any additional external power sources.     

Factors limiting current gain in power transistors

The combined effect of sidewall injection, bandgap narrowing, and Shockley-Hall-Read and Auger recombination in determining emitter efficiency in n-p-n power transistor structures is demonstrated by utilizing a two-dimensional transistor model. The relative importance of each of these effects is calculated as a function of emitter junction depth, emitter surface doping, and injection level. It is shown that in a practical transistor design the reduction in emitter efficiency due to the increased injection of holes into the emitter, resulting from bandgap narrowing caused by heavy doping, is not dominated by the emitter sidewall. Auger recombination is seen to be especially important when bandgap narrowing is present. Enhanced Auger-type recombination is due both to increased minority carrier injection in the emitter as well as current crowding effects. The predictions of the model are compared with results of the measurement of current gain versus current level characteristics on existing devices.     

Performance of iterative data detection and channel estimation for single-antenna and multiple-antennas wireless communications

In iterative data-detection and channel-estimation algorithms, the channel estimator and the data detector recursively exchange information in order to improve the system performance. While a vast bulk of the available literature demonstrates the merits of iterative schemes through computer simulations, in this paper analytical results on the performance of an iterative detection/estimation scheme are presented. In particular, this paper focus is on uncoded systems and both the situations that the receiver and the transmitter are equipped with either a single antenna or multiple antennas are considered. With regard to the channel estimator, the analysis considers both the minimum mean square error and the maximum likelihood channel estimate, while, with regard to the data detector, linear receiver interfaces are considered. Closed-form formulas are given for the channel-estimation mean-square error and for its Crame/spl acute/r-Rao bound, as well as for the error probability of the data detector. Moreover, the problem of the optimal choice of the length of the training sequence is also addressed. Overall, results show that the considered iterative strategy achieves excellent performance and permits, at the price of some complexity increase, the use of very short training sequences without incurring any performance loss. Finally, computer simulations reveal that the experimental results are in perfect agreement with those predicted by the theoretical analysis.