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

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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