A note on computing the derivative at a constant direction.
The derivative at constant direction is frequently used in inversion of cone-beam data. Several algorithms for computing the derivative have been proposed in the literature. The best algorithm to date has been proposed recently by Noo et al (2007 Phys. Med. Biol. 52 5393-414). In this note we propose a new, simple and efficient formula for computing the derivative. Numerical experiments with helical CT show that our formula and the one of Noo et al provide fairly similar spatial resolution and noise stability, even though the new formula is more efficient and easier to implement.
Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, USA. akatsevi@mail.ucf.edu
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Katsevich
D000465:Algorithms; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D013997:Time Factors; D036542:Tomography, Spiral Computed / Q000379:methods*