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 $\max\{\Phi(x),0\}$, where $\Phi$ is a smooth function. The function $\Phi$ 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.