Abstract

Co-authors: Martin Andersen (Technical University of Denmark), Yunyi Hu (Emory University)

An active area of interest in tomographic imaging is the goal of quantitative imaging, where in addition to producing an image, information about the material composition of the object is recovered. In order to obtain material composition information, it is necessary to better model of the image formation (i.e., forward) problem and/or to collect additional independent measurements. In x-ray computed tomography (CT), better modeling of the physics can be done by using the more accurate polyenergetic representation of source x-ray beams, which requires solving a challenging nonlinear ill-posed inverse problem. In this talk we explore the mathematical and computational problem of polyenergetic CT when it is used in combination with new energy-windowed spectral CT detectors. We formulate this as a regularized nonlinear least squares problem, which we solve by a Gauss-Newton scheme. Because the approximate Hessian system in the Gauss-Newton scheme is very ill-conditioned, we propose a preconditioner that effectively clusters eigenvalues and, therefore, accelerates convergence when the conjugate gradient method is used to solve the linear subsystems. Numerical experiments illustrate the convergence, effectiveness, and significance of the proposed method.