# PWLS-ULTRA: An Efficient Clustering and Learning-Based Approach for Low-Dose 3D CT Image Reconstruction

arXiv: https://arxiv.org/abs/1703.09165 · HTML: https://mlsanity.com/paper/1703.09165/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2017.

## Built on by (most cited first, 15 of 15)

- [DU-GAN: Generative Adversarial Networks with Dual-Domain U-Net Based Discriminators for Low-Dose CT Denoising](https://mlsanity.com/paper/2108.10772/) (2021)
- [Sparse-view Cone Beam CT Reconstruction using Data-consistent Supervised and Adversarial Learning from Scarce Training Data](https://mlsanity.com/paper/2201.09318/) (2022)
- [Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A survey](https://mlsanity.com/paper/2203.15725/) (2022)
- [Low-Dose CT Denoising via Sinogram Inner-Structure Transformer](https://mlsanity.com/paper/2204.03163/) (2022)
- [A Geometry-Informed Deep Learning Framework for Ultra-Sparse 3D Tomographic Image Reconstruction](https://mlsanity.com/paper/2105.11692/) (2021)
- [Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2104.12939/) (2021)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Two-and-a-half Order Score-based Model for Solving 3D Ill-posed Inverse Problems](https://mlsanity.com/paper/2308.08511/) (2023)
- [Swap-Net: A Memory-Efficient 2.5D Network for Sparse-View 3D Cone Beam CT Reconstruction](https://mlsanity.com/paper/2410.10836/) (2024)
- [Multi-Channel Convolutional Analysis Operator Learning for Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2203.05968/) (2022)
- [Multi-layer Clustering-based Residual Sparsifying Transform for Low-dose CT Image Reconstruction](https://mlsanity.com/paper/2203.11565/) (2022)
- [Self-Attention Generative Adversarial Network for Iterative Reconstruction of CT Images](https://mlsanity.com/paper/2112.12810/) (2021)
- [Enhancing Low-dose CT Image Reconstruction by Integrating Supervised and Unsupervised Learning](https://mlsanity.com/paper/2311.12071/) (2023)
- [PPORLD-EDNetLDCT: A Proximal Policy Optimization-Based Reinforcement Learning Framework for Adaptive Low-Dose CT Denoising](https://mlsanity.com/paper/2509.03185/) (2025)
- [Projection Guided Personalized Federated Learning for Low Dose CT Denoising](https://mlsanity.com/paper/2603.13422/) (2026)

## Abstract (arXiv)

The development of computed tomography (CT) image reconstruction methods that significantly reduce patient radiation exposure while maintaining high image quality is an important area of research in low-dose CT (LDCT) imaging. We propose a new penalized weighted least squares (PWLS) reconstruction method that exploits regularization based on an efficient Union of Learned TRAnsforms (PWLS-ULTRA). The union of square transforms is pre-learned from numerous image patches extracted from a dataset of CT images or volumes. The proposed PWLS-based cost function is optimized by alternating between a CT image reconstruction step, and a sparse coding and clustering step. The CT image reconstruction step is accelerated by a relaxed linearized augmented Lagrangian method with ordered-subsets that reduces the number of forward and back projections. Simulations with 2-D and 3-D axial CT scans of the extended cardiac-torso phantom and 3D helical chest and abdomen scans show that for both normal-dose and low-dose levels, the proposed method significantly improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer (PWLS-EP). PWLS with regularization based on a union of learned transforms leads to better image reconstructions than using a single learned square transform. We also incorporate patch-based weights in PWLS-ULTRA that enhance image quality and help improve image resolution uniformity. The proposed approach achieves comparable or better image quality compared to learned overcomplete synthesis dictionaries, but importantly, is much faster (computationally more efficient).