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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 29, Iss. 3 — Mar. 1, 2012
  • pp: 354–366

New error bounds for M-testing and estimation of source location with subdiffractive error

Sudhakar Prasad  »View Author Affiliations


JOSA A, Vol. 29, Issue 3, pp. 354-366 (2012)
http://dx.doi.org/10.1364/JOSAA.29.000354


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Abstract

I present new lower and upper bounds on the minimum probability of error (MPE) in Bayesian multihypothesis testing that follow from an exact integral of a version of the statistical entropy of the posterior distribution, or equivocation. I also show that these bounds are exponentially tight and thus achievable in the asymptotic limit of many conditionally independent and identically distributed measurements. I then relate the minimum mean-squared error (MMSE) and the MPE by means of certain elementary error probability integrals. In the second half of the paper, I compare the MPE and MMSE for the problem of locating a single point source with subdiffractive uncertainty. The source-strength threshold needed to achieve a desired degree of source localization seems to be far more modest than the well established threshold for the different optical super-resolution problem of disambiguating two point sources with subdiffractive separation.

© 2012 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(110.2960) Imaging systems : Image analysis
(110.3000) Imaging systems : Image quality assessment
(110.4280) Imaging systems : Noise in imaging systems

ToC Category:
Imaging Systems

History
Original Manuscript: April 14, 2011
Revised Manuscript: September 15, 2011
Manuscript Accepted: November 20, 2011
Published: March 1, 2012

Citation
Sudhakar Prasad, "New error bounds for M-testing and estimation of source location with subdiffractive error," J. Opt. Soc. Am. A 29, 354-366 (2012)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-3-354

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