# Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition

arXiv: https://arxiv.org/abs/2103.13909 · HTML: https://mlsanity.com/paper/2103.13909/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 25 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [SGD: General Analysis and Improved Rates](https://mlsanity.com/paper/1901.09401/) (2019)
- [Stochastic Gradient Descent, Weighted Sampling, and the Randomized Kaczmarz algorithm](https://mlsanity.com/paper/1310.5715/) (2013)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence](https://mlsanity.com/paper/1505.02250/) (2015)
- [An Online Plug-and-Play Algorithm for Regularized Image Reconstruction](https://mlsanity.com/paper/1809.04693/) (2018)
- [Exact and Inexact Subsampled Newton Methods for Optimization](https://mlsanity.com/paper/1609.08502/) (2016)
- [Convergence rates of sub-sampled Newton methods](https://mlsanity.com/paper/1508.02810/) (2015)
- [Block Coordinate Regularization by Denoising](https://mlsanity.com/paper/1905.05113/) (2019)
- [Sub-sampled Newton Methods with Non-uniform Sampling](https://mlsanity.com/paper/1607.00559/) (2016)
- [An Investigation of Newton-Sketch and Subsampled Newton Methods](https://mlsanity.com/paper/1705.06211/) (2017)
- [Mini-Batch Semi-Stochastic Gradient Descent in the Proximal Setting](https://mlsanity.com/paper/1504.04407/) (2015)
- [Sub-Sampled Newton Methods I: Globally Convergent Algorithms](https://mlsanity.com/paper/1601.04737/) (2016)
- [Sub-Sampled Newton Methods II: Local Convergence Rates](https://mlsanity.com/paper/1601.04738/) (2016)

## Built on by (most cited first, 3 of 3)

- [End-to-End Model-based Deep Learning for Dual-Energy Computed Tomography Material Decomposition](https://mlsanity.com/paper/2406.00479/) (2024)
- [Direct Dual-Energy CT Material Decomposition using Model-based Denoising Diffusion Model](https://mlsanity.com/paper/2507.18012/) (2025)
- [Operator Sketching for Deep Unrolling Networks](https://mlsanity.com/paper/2203.11156/) (2022)

## Abstract (arXiv)

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.