Fourier descriptors for parametric shape estimation in inverse scattering problems

Research output: Contribution to journalConference article

Abstract

We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate Cramer-Rao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions, is asymptotically achieved by the maximum likelihood estimator (MLE). Furthermore, the resultant CRB's are used to define a global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target, and facilitate geometric inferences. Numerical simulations are performed using the layer approach and the Nystrom method for computation of domain derivatives, and using Fourier descriptors for target shape parameterization. This analysis demonstrates the accuracy and generality of the proposed methods.

Original languageEnglish (US)
Pages (from-to)309-320
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4052
StatePublished - Jan 1 2000
EventSignal Processing, Sensor Fusion, and Target Recognition IX - Orlando, FL, USA
Duration: Apr 24 2000Apr 26 2000

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Fourier Descriptors
Inverse Scattering Problem
inverse scattering
Domain Derivative
Scattering
Derivatives
Cramer-Rao Lower Bound
Radar imaging
Confidence Region
Parameterization
estimators
Maximum likelihood
confidence
Nyström Method
imaging radar
Radar Imaging
Target
Unbiased estimator
Scattering Theory
Computer simulation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

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abstract = "We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate Cramer-Rao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions, is asymptotically achieved by the maximum likelihood estimator (MLE). Furthermore, the resultant CRB's are used to define a global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target, and facilitate geometric inferences. Numerical simulations are performed using the layer approach and the Nystrom method for computation of domain derivatives, and using Fourier descriptors for target shape parameterization. This analysis demonstrates the accuracy and generality of the proposed methods.",
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