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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 25 — Dec. 7, 2009
  • pp: 23213–23233

Support-assisted optical superresolution of low-resolution image sequences: the one-dimensional problem

Sudhakar Prasad and Xuan Luo  »View Author Affiliations


Optics Express, Vol. 17, Issue 25, pp. 23213-23233 (2009)
http://dx.doi.org/10.1364/OE.17.023213


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Abstract

We analyze the problem of optical superresolution (OSR) of a one-dimensional (1D) incoherent spatial signal from undersampled data when the support of the signal is known in advance. The present paper corrects and extends our previous work on the calculation of Fisher information (FI) and the associated Cramer-Rao lower bound (CRB) on the minimum error for estimating the signal intensity distribution and its Fourier components at spatial frequencies lying beyond the optical band edge. The faint-signal and bright-signal limits emerge from a unified noise analysis in which we include both additive noise of detection and shot noise of photon counting via an approximate Gaussian statistical distribution. For a large space-bandwidth product, we derive analytical approximations to the exact expressions for FI and CRB in the faint-signal limit and use them to argue why achieving any significant amount of unbiased bandwidth extension in the presence of noise is a uniquely challenging proposition. Unlike previous theoretical work on the subject of support-assisted bandwidth extension, our approach is not restricted to specific forms of the system transfer functions, and provides a unified analysis of both digital and optical superresolution of undersampled data.

© 2009 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution

ToC Category:
Image Processing

History
Original Manuscript: September 30, 2009
Revised Manuscript: November 17, 2009
Manuscript Accepted: November 18, 2009
Published: December 3, 2009

Citation
Sudhakar Prasad and Xuan Luo, "Support-assisted optical superresolution of low-resolution image sequences: the one-dimensional problem," Opt. Express 17, 23213-23233 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-25-23213


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