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Estimating random signal parameters from noisy images with nuisance parameters: linear and scanning-linear methods.
Meredith Kathryn Whitaker1, Eric Clarkson, Harrison H Barrett
1College of Optical Sciences and Department of Radiology, University of Arizona, Tucson, Arizona 85724, USA. mwhitaker@optics.arizona.edu
Optics Express
|June 12, 2008
Summary
This study compares two signal estimation methods. The Wiener estimator struggles with signal location, while a new scanning-linear estimator excels at it.
Area of Science:
- Signal processing
- Statistical estimation theory
Background:
- Object detection and parameter estimation are crucial in various scientific fields.
- Classical estimation methods like Wiener filtering have limitations in certain tasks.
- Simulating nuisance parameters with random backgrounds is essential for robust analysis.
Purpose of the Study:
- To compare the theoretical framework, implementation, and performance of two distinct estimation procedures.
- To evaluate estimators for tasks including signal location, volume, and amplitude estimation.
- To address the limitations of classical methods in signal localization.
Main Methods:
- Analysis of the classical Wiener estimator, a linear procedure minimizing mean-squared error.
- Development and evaluation of a novel scanning-linear estimator.
- Utilizing a global-extremum search by maximizing a linear metric for the scanning estimator.
Main Results:
- The Wiener estimator can determine signal amplitude and shape but fails at signal location.
- The scanning-linear estimator demonstrates significant improvements in signal location estimation.
- The scanning-linear estimator's metric is derived from maximum a posteriori (MAP) estimation under specific approximations.
Conclusions:
- Classical Wiener estimation has fundamental limitations for signal localization tasks.
- The developed scanning-linear estimator offers a superior alternative for accurate signal location.
- Further research can explore advanced data processing techniques for enhanced estimation.
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