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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 28 — Oct. 1, 2006
  • pp: 7456–7467

Regularized inversion method for retrieval of aerosol particle size distribution function in W 1,2 space

Yanfei Wang, Shufang Fan, Xue Feng, Guangjian Yan, and Yanning Guan  »View Author Affiliations

Applied Optics, Vol. 45, Issue 28, pp. 7456-7467 (2006)

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A determination of the aerosol particle size distribution function by using the particle spectrum extinction equation is an ill-posed integral equation of the first kind. To overcome this, we must incorporate regularization techniques. Most of the literature focuses on the Phillips–Twomey regularization or its variations. However, there are drawbacks for some applications in which the real aerosol distributions have large oscillations in a Junge-type distribution. The reason for this is that the scale matrix based on the norm of the second differences in the Phillips–Twomey regularization is too ill- conditioned to filter the large perturbations induced by the small algebraic spectrum of the kernel matrix and the additive noise. Therefore we reexamine the aerosol particle size distribution function retrieval problem and solve it in W1,2 space. This setting is based on Sobolev's embedding theorem in which the approximate solution best simulates the true particle size distribution functions. For choosing the regularization parameters, we also develop an a posteriori parameter choice method, which is based on the discrepancy principle. Our numerical results are based on the remote sensing data measured by the CE318 sunphotometer in Jia Xiang County, Shan Dong Province, China, and are performed to show the feasibility of the proposed algorithms.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(010.1100) Atmospheric and oceanic optics : Aerosol detection
(010.1110) Atmospheric and oceanic optics : Aerosols
(100.0100) Image processing : Image processing
(100.3190) Image processing : Inverse problems
(280.1100) Remote sensing and sensors : Aerosol detection

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: January 10, 2006
Revised Manuscript: May 7, 2006
Manuscript Accepted: May 8, 2006

Yanfei Wang, Shufang Fan, Xue Feng, Guangjian Yan, and Yanning Guan, "Regularized inversion method for retrieval of aerosol particle size distribution function in W<sup>1,2</sup> space," Appl. Opt. 45, 7456-7467 (2006)

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