Non-convexly constrained image reconstruction from nonlinear tomographic X-ray measurements

Abstract

The use of polychromatic X-ray sources in tomographic X-ray measurements leads to nonlinear X-ray transmission effects. As these nonlinearities are not normally taken into account in tomographic reconstruction, artefacts occur, which can be particularly severe when imaging objects with multiple materials of widely varying X-ray attenuation properties. In these settings, reconstruction algorithms based on a nonlinear X-ray transmission model become valuable. We here study the use of one such model and develop algorithms that impose additional non-convex constraints on the reconstruction. This allows us to reconstruct volumetric data even when limited measurements are available. We propose a nonlinear conjugate gradient iterative hard thresholding algorithm and show how many prior modelling assumptions can be imposed using a range of non-convex constraints.

Keywords: compressed sensing; inverse problems; nonlinear constrained optimization; tomography.