Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition
This work addresses computational efficiency in spectral CT material decomposition, which is incremental as it builds on existing model-based methods with a novel optimization technique.
The authors tackled the problem of efficiently reconstructing multi-material images in spectral CT by solving a regularized optimization problem using a randomized second-order method, achieving reduced computational complexity while maintaining accuracy through a non-uniform block sub-sampling approach.
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.