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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. 28, Iss. 6 — Jun. 1, 2011
  • pp: 1041–1050

Compressive imaging: hybrid measurement basis design

Amit Ashok and Mark A. Neifeld  »View Author Affiliations


JOSA A, Vol. 28, Issue 6, pp. 1041-1050 (2011)
http://dx.doi.org/10.1364/JOSAA.28.001041


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Abstract

The inherent redundancy in natural scenes forms the basis of compressive imaging where the number of measurements is less than the dimensionality of the scene. The compressed sensing theory has shown that a purely random measurement basis can yield good reconstructions of sparse objects with relatively few measurements. However, additional prior knowledge about object statistics that is typically available is not exploited in the design of the random basis. In this work, we describe a hybrid measurement basis design that exploits the power spectral density statistics of natural scenes to minimize the reconstruction error by employing an optimal combination of a nonrandom basis and a purely random basis. Using simulation studies, we quantify the reconstruction error improvement achievable with the hybrid basis for a diverse set of natural images. We find that the hybrid basis can reduce the reconstruction error up to 77% or equivalently requires fewer measurements to achieve a desired reconstruction error compared to the purely random basis. It is also robust to varying levels of object sparsity and yields as much as 40% lower reconstruction error compared to the random basis in the presence of measurement noise.

© 2011 Optical Society of America

OCIS Codes
(100.0100) Image processing : Image processing
(100.6640) Image processing : Superresolution
(110.0110) Imaging systems : Imaging systems
(110.1758) Imaging systems : Computational imaging

ToC Category:
Imaging Systems

History
Original Manuscript: February 2, 2011
Manuscript Accepted: March 9, 2011
Published: May 17, 2011

Virtual Issues
Vol. 6, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Amit Ashok and Mark A. Neifeld, "Compressive imaging: hybrid measurement basis design," J. Opt. Soc. Am. A 28, 1041-1050 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-6-1041


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