Regularized Newton Sketch by Denoising Score Matching for Computed Tomography Reconstruction

In this work we aim at efficiently solving a model-based maximum-a-posterior (MAP) image reconstruction with application to low-dose transmission X-ray Computed tomography (CT). We propose to solve the regularized optimization problem by a randomized second order method called Newton iterative Hessian sketching for the Poisson likelihood function and to design a regularization term for the MAP problem exploiting the denoising score framework.

By approximating the Newton step using a partial Hessian sketch only for the data fit term, it is possible to reduce the complexity by dimensionality reduction while retaining the complex prior structure by a data-driven regularizer. This work shows how to use partial Netwon sketch with denoising score matching and how to efficiently compute the gradient and the Hessian of the likelihood and regularizer.

Finally, we show an example for monoenergetic X-ray CT reconstruction.