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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 9 — Oct. 3, 2011

Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing

Yoav Shechtman, Yonina C. Eldar, Alexander Szameit, and Mordechai Segev  »View Author Affiliations


Optics Express, Vol. 19, Issue 16, pp. 14807-14822 (2011)
http://dx.doi.org/10.1364/OE.19.014807


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Abstract

We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The reconstruction method relies on the recently demonstrated sparsity-based sub-wavelength imaging. However, for partially-spatially-incoherent light, the relation between the measurements and the image is quadratic, yielding non-convex measurement equations that do not conform to previously used techniques. Consequently, we demonstrate new algorithmic methodology, referred to as quadratic compressed sensing, which can be applied to a range of other problems involving information recovery from partial correlation measurements, including when the correlation function has local dependencies. Specifically for microscopy, this method can be readily extended to white light microscopes with the additional knowledge of the light source spectrum.

© 2011 OSA

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(110.4980) Imaging systems : Partial coherence in imaging
(180.0180) Microscopy : Microscopy

ToC Category:
Microscopy

History
Original Manuscript: April 26, 2011
Revised Manuscript: June 23, 2011
Manuscript Accepted: June 24, 2011
Published: July 18, 2011

Virtual Issues
Vol. 6, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Yoav Shechtman, Yonina C. Eldar, Alexander Szameit, and Mordechai Segev, "Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing," Opt. Express 19, 14807-14822 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-16-14807


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