Title

Noise enhanced signal detection and estimation

Date of Award

2007

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical Engineering and Computer Science

Advisor(s)

Pramod K. Varshney

Keywords

Signal detection, Noise-enhanced effect

Subject Categories

Electrical and Computer Engineering | Engineering

Abstract

This dissertation investigates the phenomenon of noise enhanced systems (PHONES) for a variety of signal processing problems and systems, including the general two hypotheses signal detection problem, nonparametric detection, distributed detection, the parameter estimation problem and a broad group of image processing systems. The mathematical framework to analyze the noise enhanced effect in binary hypothesis testing problems is developed and the mechanism for noise enhanced signal detection is explored. The detector optimization problem under both Neyman-Pearson and Bayesian criteria is examined. The optimal noise pdf, the corresponding detector and the maximum achievable performance are determined.

Potential improvement of nonparametric detection performance via adding noise is analyzed. Asymptotic as well as finite sample size detection performances are evaluated. Conditions for improvability as well as the optimum additive noise distributions of the sign detector, the Wilcoxon detector, the dead-zone limiter detector and the Polarity Coincidence Correlator (PCC) detector are derived. A learning algorithm to find the optimal noise distribution based on unlabeled received data is proposed for the case where the underlying distributions for both hypotheses are unknown. Two types of noise enhanced systems are proposed for the distribution detection problem and improvements for both cases are demonstrated even for a seemingly optimum system. The optimum noise pdfs for both systems are derived. For the general noise enhanced parameter estimation problem where the noise can be introduced via a random transformation, investigation is carried out to find the optimum noise pdf and the best achievable performance. Approaches are also proposed to find the optimum noise when the estimator is unknown.

Potential enhancement of image processing systems via the addition of noise is also investigated. For the noise modified image processing system via the addition of a single image, the best achievable performance is shown to be obtained by adding a constant image to the observed image. A multiple noise modified image processing system is proposed to counter this difficulty and to provide a robust performance even when the testing image statistics are different than expected.

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