Limited Data X-Ray Tomography Using Nonlinear Evolution Equations

A novel approach to the X-ray tomography problem with sparse projection data is proposed. Non-negativity of the X-ray attenuation coefficient is enforced by modelling it as max{(x), 0} where is a smooth function. The function is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods. The reconstruction algorithm is applied to (a) simulated full and limited angle projection data of the Shepp-Logan phantom with sparse angular sampling and (b) measured limited angle projection data of in vitro dental specimens. The results are significantly better than those given by traditional backprojection-based approaches, and similar in quality (but faster to compute) compared to Algebraic Reconstruction Technique (ART). Key words. Limited angle tomography, X-ray tomography, level set, nonlinear evolution equation AMS subject classifications. 44A12, 92C55, 65N21, 65R32 Revision 10: May 15, 2007

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Ville Kolehmainen, Matti Lassas, Samuli Siltanen
• Keywords: Angle Projection Data, Limited Angle Projection, Projection Data, SIAMSC 2008