Maximum-likelihood time-of-arrival estimation for saturated optical transient signals.

We employ right-censored Poisson point process models to develop maximum-likelihood procedures for estimating the time of arrival of transient optical signals subject to saturation distortion. The Poisson intensity is modeled as a template with an unknown scaling factor with additive background counts. Using Monte Carlo simulations, we explore the performance of different algorithms as a function of signal magnitude and saturation threshold. In particular, we characterize the benefit our procedures have over algorithms that are unaware of the censoring.

Expectation-maximization algorithm for amplitude estimation of saturated optical transient signals.

This paper addresses parameter estimation for an optical transient signal when the received data has been right-censored. We develop an expectation-maximization (EM) algorithm to estimate the amplitude of a Poisson intensity with a known shape in the presence of additive background counts, where the measurements are subject to saturation effects. We compare the results of our algorithm with those of an EM algorithm that is unaware of the censoring.

Phase retrieval from noisy data based on minimization of penalized I-divergence.

We study noise artifacts in phase retrieval based on minimization of an information-theoretic discrepancy measure called Csiszár's I-divergence. We specifically focus on adding Poisson noise to either the autocorrelation of the true image (as in astronomical imaging through turbulence) or the squared Fourier magnitudes of the true image (as in x-ray crystallography). Noise effects are quantified via various error metrics as signal-to-noise ratios vary. We propose penalized minimum I-divergence methods to suppress the observed noise artifacts. To avoid computational difficulties arising from the introduction of a penalty, we adapt Green's one-step-late approach for use in our minimum I-divergence framework.

Convergence of the Schulz-Snyder phase retrieval algorithm to local minima.

The Schulz-Snyder iterative algorithm for phase retrieval attempts to recover a nonnegative function from its autocorrelation by minimizing the I-divergence between a measured autocorrelation and the autocorrelation of the estimated image. We illustrate that the Schulz-Snyder algorithm can become trapped in a local minimum of the I-divergence surface. To show that the estimates found are indeed local minima, sufficient conditions involving the gradient and the Hessian matrix of the I-divergence are given. Then we build a brief proof showing how an estimate that satisfies these conditions is a local minimum. The conditions are used to perform numerical tests determining local minimality of estimates. Along with the tests, related numerical issues are examined, and some interesting phenomena are discussed.