Detection and Estimation of Abrupt Changes contaminated by Multiplicative Gaussian Noise

The problem of abrupt change detection has received much attention in the literature. The Neyman Pearson detector can be derived and yields the well-known CUSUM algorithm, when the abrupt change is contaminated by an additive noise. However, a multiplicative noise has been observed in many signal processing applications. These applications include radar, sonar, communication and image processing. This paper addresses the problem of abrupt change detection in presence of multiplicative noise. The optimal Neyman Pearson detector is studied when the abrupt change and noise parameters are known. The parameters are unknown in most practical applications and have to be estimated. The maximum likelihood estimator is then derived for these parameters. The maximum likelihood estimator performance is determined, by comparing the estimate mean square errors with the Cramer Rao Bounds. The Neyman Pearson detector combined with the maximum likelihood estimator yields the generalized likelihood ratio detector

Parametric modeling of photometric signals

This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The Cramér Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The Neyman–Pearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The Neyman–Pearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations

High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an N-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime i.e., when the number N of quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of non-independent observations. If d represents the dimension of one sample, it is proved that the error exponent converges at rate N^{2/d} to the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.Comment: 47 pages, 7 figures, 1 table. To appear in the IEEE Transactions on Information Theor