Estimating random signal parameters from noisy images with nuisance parameters

Linear and scanning-linear methods

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

In a pure estimation task, an object of interest is known to be present, and we wish to determine numerical values for parameters that describe the object. This paper compares the theoretical framework, implementation method, and performance of two estimation procedures. We examined the performance of these estimators for tasks such as estimating signal location, signal volume, signal amplitude, or any combination of these parameters. The signal is embedded in a random background to simulate the effect of nuisance parameters. First, we explore the classical Wiener estimator, which operates linearly on the data and minimizes the ensemble mean-squared error. The results of our performance tests indicate that the Wiener estimator can estimate amplitude and shape once a signal has been located, but is fundamentally unable to locate a signal regardless of the quality of the image. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanning-linear estimator that performs impressively for location estimation. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly varying covariance approximation is made.

Original languageEnglish (US)
Pages (from-to)8150-8173
Number of pages24
JournalOptics Express
Volume16
Issue number11
DOIs
StatePublished - May 26 2008

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random signals
estimators
estimating
scanning
performance tests
range (extremes)
estimates
approximation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "In a pure estimation task, an object of interest is known to be present, and we wish to determine numerical values for parameters that describe the object. This paper compares the theoretical framework, implementation method, and performance of two estimation procedures. We examined the performance of these estimators for tasks such as estimating signal location, signal volume, signal amplitude, or any combination of these parameters. The signal is embedded in a random background to simulate the effect of nuisance parameters. First, we explore the classical Wiener estimator, which operates linearly on the data and minimizes the ensemble mean-squared error. The results of our performance tests indicate that the Wiener estimator can estimate amplitude and shape once a signal has been located, but is fundamentally unable to locate a signal regardless of the quality of the image. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanning-linear estimator that performs impressively for location estimation. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly varying covariance approximation is made.",
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