Below is a list of algorithms for tomographic data processing, in order of number of software packages that implement them. For more information about each package, you can click on the Tomopedia link.

Direct algorithms

Name Software Description References
Filtered Backprojection     [Kak+01]
Gridrec     [Dow+99], [Mar+12]

Iterative algorithms

Name Software Description References
SIRT   Simultaneous Iterative Reconstruction Technique [Kak+01]
ART   Algebraic Reconstruction Technique [Kak+01]


References

[Dow+99] Dowd BA, Campbell GH, Marr RB, Nagarkar VV, Tipnis SV, Axe L, and Siddons DP. Developments in synchrotron x-ray computed microtomography at the national synchrotron light source. In Proc. SPIE, volume 3772, 224–236. 1999.
[Kak+01] Kak, A. C., & Slaney, M. (2001). Principles of Computerized Tomographic Imaging (Philadelphia, PA: SIAM).
[Mar+12] Marone, F., & Stampanoni, M. (2012). Regridding reconstruction algorithm for real-time tomographic imaging. Journal of synchrotron radiation, 19(6), 1029-1037.