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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 10 — Apr. 1, 2013
  • pp: D32–D45

Fast lapped block reconstructions in compressive spectral imaging

Henry Arguello, Claudia V. Correa, and Gonzalo R. Arce  »View Author Affiliations


Applied Optics, Vol. 52, Issue 10, pp. D32-D45 (2013)
http://dx.doi.org/10.1364/AO.52.000D32


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Abstract

The coded aperture snapshot spectral imager (CASSI) senses the spatial and spectral information of a scene using a set of K random projections of the scene onto focal plane array measurements. The reconstruction of the underlying three-dimensional (3D) scene is then obtained by 1 norm-based inverse optimization algorithms such as the gradient projections for sparse reconstruction (GPSR). The computational complexity of the inverse problem in this case grows with order O ( K N 4 L ) per iteration, where N 2 and L are the spatial and spectral dimensions of the scene, respectively. In some applications the computational complexity becomes overwhelming since reconstructions can take up to several hours in desktop architectures. This paper presents a mathematical model for lapped block reconstructions in CASSI with O ( K B 4 L ) complexity per GPSR iteration where B N is the block size. The approach takes advantage of the structure of the sensing matrix thus allowing the independent recovery of smaller overlapping blocks spanning the measurement set. The reconstructed 3D lapped parallelepipeds are then merged to reduce the block-artifacts in the reconstructed scenes. The full data cube is reconstructed with complexity O ( K ( N 4 / ( N ) 2 ) L ) , per iteration, where N = N / B . Simulations show the benefits of the new model as data cube reconstruction can be accelerated by an order of magnitude. Furthermore, the lapped block reconstructions lead to comparable or higher image reconstruction quality.

© 2013 Optical Society of America

OCIS Codes
(110.1758) Imaging systems : Computational imaging
(110.4234) Imaging systems : Multispectral and hyperspectral imaging

History
Original Manuscript: November 16, 2012
Revised Manuscript: February 21, 2013
Manuscript Accepted: February 21, 2013
Published: March 20, 2013

Citation
Henry Arguello, Claudia V. Correa, and Gonzalo R. Arce, "Fast lapped block reconstructions in compressive spectral imaging," Appl. Opt. 52, D32-D45 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-10-D32

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