A constrained Gauss-Newton algorithm for material decomposition in spectral computed tomography

Tom Hohweiller, Nicolas Ducros, Françoise Peyrin, Bruno Sixou

Abstract: Spectral computed tomography exploits energy-resolved detectors to recover the material composition of an object. Material decomposition is a challenging nonlinear and ill-posed inverse problem. While regularization improves the decomposition, the resulting material maps do not satisfy physical constraints (e.g., positivity). In this work, we propose a fast second-order algorithm for constrained material decomposition. The proposed constrained Gauss-Newton algorithm is compared to a standard (unconstrained) Gauss-Newton algorithm on two realistic numerical phantoms. An improved decomposition is obtained for both phantoms. We also found that the constraints must be enforced progressively during the iterations.