# Deep Learning for Material Decomposition in Photon-Counting CT

arXiv: https://arxiv.org/abs/2208.03360 · HTML: https://mlsanity.com/paper/2208.03360/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 5 Aug 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [The state of the art in kidney and kidney tumor segmentation in contrast-enhanced CT imaging: Results of the KiTS19 Challenge](https://mlsanity.com/paper/1912.01054/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [Learned convex regularizers for inverse problems](https://mlsanity.com/paper/2008.02839/) (2020)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation](https://mlsanity.com/paper/1906.07499/) (2019)
- [Data-driven nonsmooth optimization](https://mlsanity.com/paper/1808.00946/) (2018)
- [Machine Friendly Machine Learning: Interpretation of Computed Tomography Without Image Reconstruction](https://mlsanity.com/paper/1812.01068/) (2018)
- [AAPM DL-Sparse-View CT Challenge Submission Report: Designing an Iterative Network for Fanbeam-CT with Unknown Geometry](https://mlsanity.com/paper/2106.00280/) (2021)
- [Deep learning based dictionary learning and tomographic image reconstruction](https://mlsanity.com/paper/2108.11730/) (2021)

## Built on by (most cited first, 2 of 2)

- [CT Material Decomposition using Spectral Diffusion Posterior Sampling](https://mlsanity.com/paper/2402.03476/) (2024)
- [A Dual-domain Refinement Network with FBP-based Jacobian Learning for Sparse-view Dual-Energy CT Material Decomposition](https://mlsanity.com/paper/2606.30159/) (2026)

## Abstract (arXiv)

Photon-counting CT (PCCT) offers improved diagnostic performance through better spatial and energy resolution, but developing high-quality image reconstruction methods that can deal with these large datasets is challenging. Model-based solutions incorporate models of the physical acquisition in order to reconstruct more accurate images, but are dependent on an accurate forward operator and present difficulties with finding good regularization. Another approach is deep-learning reconstruction, which has shown great promise in CT. However, fully data-driven solutions typically need large amounts of training data and lack interpretability. To combine the benefits of both methods, while minimizing their respective drawbacks, it is desirable to develop reconstruction algorithms that combine both model-based and data-driven approaches. In this work, we present a novel deep-learning solution for material decomposition in PCCT, based on an unrolled/unfolded iterative network. We evaluate two cases: a learned post-processing, which implicitly utilizes model knowledge, and a learned gradient-descent, which has explicit model-based components in the architecture. With our proposed techniques, we solve a challenging PCCT simulation case: three-material decomposition in abdomen imaging with low dose, iodine contrast, and a very small training sample support. In this scenario, our approach outperforms a maximum likelihood estimation, a variational method, as well as a fully-learned network.