Abstract

Ben-David and Ren [Appl. Opt. 44, 3846 (2005)] discussed methods of estimating the concentration of chemical vapor plumes in hyperspectral images. The authors of that paper concluded that a technique called orthogonal subspace projection (OSP) produces better concentration estimates than background subtraction when certain stochastic noise conditions are present in the data. While that conclusion is correct, it is worth noting that the data can be whitened to improve the performance of the background subtraction method. In particular, if the noise is multivariate Gaussian, then whitening will ensure that the background subtraction method is superior to OSP.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Ben-David and H. Ren, "Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data," Appl. Opt. 44, 3846-3855 (2005).
    [CrossRef] [PubMed]
  2. A. Ben-David and H. Ren, "Detection, identification, and estimation of biological aerosols and vapors with a Fourier-transform infrared spectrometer," Appl. Opt. 42, 4887-4900 (2003).
    [CrossRef] [PubMed]
  3. S. Kraut, L. Scharf, and L. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
    [CrossRef]
  4. G. Casella and R. L. Berger, Statistical Inference (Duxbury Press, 2002).

2005 (1)

2003 (1)

2001 (1)

S. Kraut, L. Scharf, and L. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Ben-David, A.

Berger, R. L.

G. Casella and R. L. Berger, Statistical Inference (Duxbury Press, 2002).

Casella, G.

G. Casella and R. L. Berger, Statistical Inference (Duxbury Press, 2002).

Kraut, S.

S. Kraut, L. Scharf, and L. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

McWhorter, L.

S. Kraut, L. Scharf, and L. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Ren, H.

Scharf, L.

S. Kraut, L. Scharf, and L. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (9)

Equations on this page are rendered with MathJax. Learn more.

r = b + d α + n ,
α ^ sub = d T ( r b ) d T d .
α ^ OSP = d T P b r d T P b d ,
r N [ b + d α , C ] .
l ( α ; r ) = 1 / 2 ln ( | 2 π C | ) 1 / 2 [ ( r b d α ) T × C 1 ( r b d α ) ] .
l ( α ; r ) α = α d T C 1 d + r T C 1 d b T C 1 d .
α ^ = d T C 1 ( r b ) d T C 1 d .
α ^ N [ α , 1 d T C 1 d ] .
Var [ d T C 1 ( r b ) d T C 1 d ] Var [ d T P b r d T P b d ] .

Metrics