  Spectral Computed Tomography (CT) is an emerging technology that enables to
estimate the concentration of basis materials within a scanned object by
exploiting different photon energy spectra. In this work, we aim at efficiently
solving a model-based maximum-a-posterior problem to reconstruct
multi-materials images with application to spectral CT. In particular, we
propose to solve a regularized optimization problem based on a plug-in
image-denoising function using a randomized second order method. By
approximating the Newton step using a sketching of the Hessian of the
likelihood function, it is possible to reduce the complexity while retaining
the complex prior structure given by the data-driven regularizer. We exploit a
non-uniform block sub-sampling of the Hessian with inexact but efficient
Conjugate gradient updates that require only Jacobian-vector products for
denoising term. Finally, we show numerical and experimental results for
spectral CT materials decomposition.
