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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

  • Vol. 16, Iss. 12 — Dec. 1, 1999
  • pp: 2896–2903

Minimal-scan filtered backpropagation algorithms for diffraction tomography

Xiaochuan Pan and Mark A. Anastasio  »View Author Affiliations


JOSA A, Vol. 16, Issue 12, pp. 2896-2903 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002896


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Abstract

The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging 4, 336 (1982)], has been widely used for reconstructing images in diffraction tomography. It is generally known that the FBPP algorithm requires scattered data from a full angular range of 2π for exact reconstruction of a generally complex-valued object function. However, we reveal that one needs scattered data only over the angular range 0ϕ3π/2 for exact reconstruction of a generally complex-valued object function. Using this insight, we develop and analyze a family of minimal-scan filtered backpropagation (MS-FBPP) algorithms, which, unlike the FBPP algorithm, use scattered data acquired from view angles over the range 0ϕ3π/2. We show analytically that these MS-FBPP algorithms are mathematically identical to the FBPP algorithm. We also perform computer simulation studies for validation, demonstration, and comparison of these MS-FBPP algorithms. The numerical results in these simulation studies corroborate our theoretical assertions.

© 1999 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6950) Image processing : Tomographic image processing

History
Original Manuscript: March 31, 1999
Revised Manuscript: August 12, 1999
Manuscript Accepted: August 12, 1999
Published: December 1, 1999

Citation
Xiaochuan Pan and Mark A. Anastasio, "Minimal-scan filtered backpropagation algorithms for diffraction tomography," J. Opt. Soc. Am. A 16, 2896-2903 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-12-2896

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