Limited Data X-Ray Tomography Using Nonlinear Evolution Equations

A novel approach to the X-ray tomography problem with sparse projection data is proposed. Nonnegativity of the X-ray attenuation coefficient is enforced by modelling it as max\Φ(x),0\, where Φ is a smooth function. The function Φ 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 the algebraic reconstruction technique.