Nonlinear optimization for mixed attenuation polyenergetic image reconstruction

Abstract

With the emergence of new computed tomography (CT) machines, polyenergetic image reconstruction has become increasingly popular in recent years. By solving a nonlinear equation, we can obtain not only the visual structure of the object, but also quantitative information about the materials in the object. In this paper, we revisit the multi-material polyenergetic model and transform it into a nonlinear optimization problem that involves both equality and inequality constraints. In order to keep the second-order derivative positive semi-definite, we propose a modified Hessian. In addition to the modified Hessian, a problem-specific nonlinear interior-point method is implemented to solve this problem. Moreover, total variation regularization is applied to stabilize the solutions. Both for full CT and limited angle cases, we can obtain images of high quality with this method. Numerical experiments illustrate the convergence, effectiveness, and significance of the proposed method.