Minimal-scan filtered backpropagation algorithms for diffraction tomography

Xiaochuan Pan, Mark A. Anastasio

Research output: Contribution to journalArticlepeer-review


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 0 ≤ ø ≤ 3π/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 0 ≤ ø ≤ 3π/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.

Original languageEnglish (US)
Pages (from-to)2896-2903
Number of pages8
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number12
StatePublished - Dec 1999
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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