Donald L. Snyder

Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography

Reconstruction procedures that account for attenuation in forming maximum-likelihood estimates of activity distributions in positron-emission tomography are extended to include regularization constraints and accidental coincidences. A mathematical model is used for these effects. The corrections are incorporated into the iterations of an expectation-maximization algorithm for numerically producing the maximum-likelihood estimate of the distribution of radioactivity within a patient. The images reconstructed with this procedure are unbiased and exhibit lower variance than those reconstructed from precorrected data.

The expectation-maximization algorithm for symbol unsynchronized sequence detection

The expectation-maximization (EM) algorithm for maximizing likelihood functions, combined with the Viterbi algorithm, is applied to the problem of sequence detection when symbol timing information is not present. Although the EM algorithm is noncausal, results obtained using the algorithm on the problem of nonsynchronized sequence detection indicate that it converges most of the time in three iterations, making it both of theoretical and of practical interest. A practical algorithm based on the EM algorithm is introduced. It reduces the computational burden and improves performance by making use of timing estimates in previous observation windows. >

The use of maximum likelihood estimation for forming images of diffuse radar targets from delay-Doppler data

An approach to high-resolution imaging that starts with a model of the radar echo signal derived from the physics governing radar reflections is presented. The model has been used in the past to describe radar targets that are rough compared to the wavelength of the transmitted radiation. Without specifying precisely what the transmitted signal is, a general estimation-based procedure is derived for obtaining images. After discretizing the model, the radar imaging problem reduces to the task of estimating discretized second-order statistics of the reflectance process of the target. Maximum-likelihood estimates of these statics are obtained as the limit point of an expectation-maximization algorithm. >

An evaluation of maximum likelihood reconstruction for SPECT

A reconstruction method for SPECT (single photon emission computerized tomography) that uses the maximum likelihood (ML) criterion and an iterative expectation-maximization (EM) algorithm solution is examined. The method is based on a model that incorporates the physical effects of photon statistics, nonuniform photon attenuation, and a camera-dependent point-spread response function. Reconstructions from simulation experiments are presented which illustrate the ability of the ML algorithm to correct for attenuation and point-spread. Standard filtered backprojection method reconstructions, using experimental and simulated data, are included for reference. Three studies were designed to focus on the effects of noise and point-spread, on the effect of nonuniform attenuation, and on the combined effects of all three. The last study uses a chest phantom and simulates Tl-201 imaging of the myocardium. A quantitative analysis of the reconstructed images is used to support the conclusion that the ML algorithm produces reconstructions that exhibit improved signal-to-noise ratios, improved image resolution, and image quantifiability.

Locating Data Frames in Direct-Detection Optical Communication Systems

The maximum-likelihood rule for locating a frame-synchronization pattern in a direct-detection optical communication system employing either Q -ary pulse-position modulation or on-off keying is identified. We show that equivalent performance for the simple correlation and postdctection-correlation rules used in practice can require substantially more than a 3 dB increase in signal power over that required using the maximum-likelihood rule.

High-resolution imaging at low-light levels through weak turbulence

Measurements of an object viewed at low-light levels through weak atmospheric turbulence are modeled mathematically as a time-space doubly stochastic Poisson process in which the intensity function moves randomly in time but is otherwise undistorted. This model is used with the maximum-likelihood method of statistics to derive a new method for forming an image of the object. A simple computer simulation of a moving one-dimensional binary star suggests that improved images may be produced by this method in comparison with others that have been suggested in the literature, but it remains to be demonstrated that this improvement is realized in practice with real imagery data.

Design of Coding and Modulation for Power-Efficient Use of a Band-Limited Optical Channel

We show that Q -ary pulse-position modulation with raised cosine pulses minimizes the average power (photons/s) required to communicate at a specified throughput rate (nats/s) over a band-limited, noisy optical channel. The best choice of Q is identified, as are other encoder parameters.

Receiver Performance for Heterodyne Optical Communication

A model for the heterodyne optical channel that is consistent with experimental observations is introduced, and a general maximum-likelihood sequence estimation receiver that accounts for laser phase instabilities is proposed using the generalized log-likelihood functional. The performance of various suboptimal estimator-correlator receivers, obtained from optimal, nonimplementable receiver equations, is studied by simulation and compared to that of an incoherent receiver for practical parameter values. It is observed that, for hard decisions, the proposed receiver performs significantly better than an incoherent receiver for bit intervals larger than about half the coherence time of the laser oscillators, with larger gains to be expected when soft decisions on long sequences are made. A way of reducing the complexity of the soft-decisions receiver for long sequences is discussed.

A Proposed Receiver Structure for Optical Communication Systems that Employ Heterodyne Detection and a Semiconductor Laser as a Local Oscillator

Coherent heterodyne detection in optical communication is degraded by phase instabilities present when a semiconductor laser is used as a local oscillator. Postdetection processing that accounts for these instabilities is suggested, based on a diffusion-process model for oscillator instabilities and a maximum-likelihood sequence-estimator of information symbols modulating the received light.

Phase and Frequency Tracking Accuracy in Direct-Detection Optical-Communication Systems

Lower bounds are given on the attainable mean-square performance in causally tracking the phase and frequency of a subcarrier that modulates an optical carrier in a direct-detection opticalcommunication system.