# Unsupervised denoising for sparse multi-spectral computed tomography

arXiv: https://arxiv.org/abs/2211.01159 · HTML: https://mlsanity.com/paper/2211.01159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Low Dose CT Image Denoising Using a Generative Adversarial Network with Wasserstein Distance and Perceptual Loss](https://mlsanity.com/paper/1708.00961/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [3D Convolutional Encoder-Decoder Network for Low-Dose CT via Transfer Learning from a 2D Trained Network](https://mlsanity.com/paper/1802.05656/) (2018)
- [Unsupervised Learning with Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/1805.10531/) (2018)
- [Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography](https://mlsanity.com/paper/1307.5348/) (2013)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [An Educated Warm Start For Deep Image Prior-Based Micro CT Reconstruction](https://mlsanity.com/paper/2111.11926/) (2021)
- [Sparse-View Spectral CT Reconstruction Using Deep Learning](https://mlsanity.com/paper/2011.14842/) (2020)
- [Multi-Spectral Imaging via Computed Tomography (MUSIC) - Comparing Unsupervised Spectral Segmentations for Material Differentiation](https://mlsanity.com/paper/1810.11823/) (2018)

## Built on by (most cited first, 1 of 1)

- [SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography](https://mlsanity.com/paper/2604.15651/) (2026)

## Abstract (arXiv)

Multi-energy computed tomography (CT) with photon counting detectors (PCDs) enables spectral imaging as PCDs can assign the incoming photons to specific energy channels. However, PCDs with many spectral channels drastically increase the computational complexity of the CT reconstruction, and bespoke reconstruction algorithms need fine-tuning to varying noise statistics. revEspecially if many projections are taken, a large amount of data has to be collected and stored. Sparse view CT is one solution for data reduction. However, these issues are especially exacerbated when sparse imaging scenarios are encountered due to a significant reduction in photon counts. In this work, we investigate the suitability of learning-based improvements to the challenging task of obtaining high-quality reconstructions from sparse measurements for a 64-channel PCD-CT. In particular, to overcome missing reference data for the training procedure, we propose an unsupervised denoising and artefact removal approach by exploiting different filter functions in the reconstruction and an explicit coupling of spectral channels with the nuclear norm. Performance is assessed on both simulated synthetic data and the openly available experimental Multi-Spectral Imaging via Computed Tomography (MUSIC) dataset. We compared the quality of our unsupervised method to iterative total nuclear variation regularized reconstructions and a supervised denoiser trained with reference data. We show that improved reconstruction quality can be achieved with flexibility on noise statistics and effective suppression of streaking artefacts when using unsupervised denoising with spectral coupling.