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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 31 — Nov. 1, 2010
  • pp: 6140–6148

Estimating the noise variance in an image acquisition system and its influence on the accuracy of recovered spectral reflectances

Mikiya Hironaga and Noriyuki Shimano  »View Author Affiliations


Applied Optics, Vol. 49, Issue 31, pp. 6140-6148 (2010)
http://dx.doi.org/10.1364/AO.49.006140


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Abstract

It is well known that the noise present in an image acquisition system plays important roles in solving inverse problems, such as the reconstruction of spectral reflectances of imaged objects from the sensor responses. Usually, a recovered spectral reflectance vector r ^ by a matrix W is expressed by r ^ = W p , where p is a sensor response vector. In this paper, the mean square errors (MSEs) between the recovered spectral reflectances with various reconstruction matrices W and actual spectral reflectances are divided into the noise independent MSE ( MSE FREE ) and the noise dependent MSE ( MSE NOISE ). By dividing the MSE into two terms, the MSE NOISE is defined as the estimated noise variance multiplied by the sum of the squared singular values of the matrix W. It is shown that the relation between the increase in the MSE and the MSE NOISE agrees quite well with the experimental results by the multispectral camera, and that the estimated noise variances are of the same order of magnitude for various matrices W, but the increase in the MSE by the noise mainly results from the increase in the sum of the squared singular values for the unregularized reconstruction matrix W.

© 2010 Optical Society of America

OCIS Codes
(110.4280) Imaging systems : Noise in imaging systems
(150.0150) Machine vision : Machine vision
(330.6180) Vision, color, and visual optics : Spectral discrimination

ToC Category:
Imaging Systems

History
Original Manuscript: August 3, 2010
Manuscript Accepted: September 6, 2010
Published: October 28, 2010

Virtual Issues
Vol. 6, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Mikiya Hironaga and Noriyuki Shimano, "Estimating the noise variance in an image acquisition system and its influence on the accuracy of recovered spectral reflectances," Appl. Opt. 49, 6140-6148 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-31-6140


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