An active area of interest in to mographic imaging is the goal of quantitative imag ing\, where in addition to producing an image\, in formation about the material composition of the ob ject is recovered. In order to obtain material com position information\, it is necessary to better m odel of the image formation (i.e.\, forward) probl em and/or to collect additional independent measur ements. In x-ray computed tomography (CT)\, better modeling of the physics can be done by using the more accurate polyenergetic representation of sour ce x-ray beams\, which requires solving a challeng ing nonlinear ill-posed inverse problem. In this t alk we explore the mathematical and computational problem of polyenergetic CT when it is used in com bination with new energy-windowed spectral CT dete ctors. We formulate this as a regularized nonlinea r least squares problem\, which we solve by a Gaus s-Newton scheme. Because the approximate Hessian s ystem in the Gauss-Newton scheme is very ill-condi tioned\, we propose a preconditioner that effectiv ely clusters eigenvalues and\, therefore\, acceler ates convergence when the conjugate gradient metho d is used to solve the linear subsystems. Numerica l experiments illustrate the convergence\, effecti veness\, and significance of the proposed method.< /span> LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR