PDE-based numerical method for a limited angle X-ray tomography

Abstract

A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing the X-ray tomography rather than on the conventional integral formulation. The quasi-reversibility method is applied. Convergence analysis is performed using a new Carleman estimate. Numerical results are presented and compared with the inversion of the Radon transform using the well-known filtered back projection algorithm. In addition, it is shown how to use our method to study the inversion of the attenuated X-ray transform for the same case of incomplete data.

References in corpus (2)

• Convexification of Restricted Dirichlet-to-Neumann Map
• A new version of the convexification method for a 1-D coefficient inverse problem with experimental data

Cited by in corpus (3)

• A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data
• A convergent numerical method for a multi-frequency inverse source problem in inhomogenous media
• The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data