The filtered backpropagation (FBPP) algorithm, originally developed by Devaney [Ultrason. Imaging <b>4</b>, 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≤φ≤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≤φ≤ 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.
© 1999 Optical Society of America
Xiaochuan Pan and Mark A. Anastasio, "Minimal-scan filtered backpropagation algorithms for diffraction tomography," J. Opt. Soc. Am. A 16, 2896-2903 (1999)