# Equivariant Multiscale Learned Invertible Reconstruction for Cone Beam CT: From Simulated to Real Data

arXiv: https://arxiv.org/abs/2512.21180 · HTML: https://mlsanity.com/paper/2512.21180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Multi-Scale Learned Iterative Reconstruction](https://mlsanity.com/paper/1908.00936/) (2019)
- [Deep learning reconstruction of digital breast tomosynthesis images for accurate breast density and patient-specific radiation dose estimation](https://mlsanity.com/paper/2006.06508/) (2020)
- [Joint Supervised and Self-supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2311.15856/) (2023)

## Abstract (arXiv)

Cone Beam CT (CBCT) is an important imaging modality nowadays, however lower image quality of CBCT compared to more conventional Computed Tomography (CT) remains a limiting factor in CBCT applications. Deep learning reconstruction methods are a promising alternative to classical analytical and iterative reconstruction methods, but applying such methods to CBCT is often difficult due to the lack of ground truth data, memory limitations and the need for fast inference at clinically-relevant resolutions. In this work we propose LIRE++, an end-to-end rotationally-equivariant multiscale learned invertible primal-dual scheme for fast and memory-efficient CBCT reconstruction. Memory optimizations and multiscale reconstruction allow for fast training and inference, while rotational equivariance improves parameter efficiency. LIRE++ was trained on simulated projection data from a fast quasi-Monte Carlo CBCT projection simulator that we developed as well. Evaluated on synthetic data, LIRE++ gave an average improvement of 1 dB in Peak Signal-to-Noise Ratio over alternative deep learning baselines. On real clinical data, LIRE++ improved the average Mean Absolute Error between the reconstruction and the corresponding planning CT by 10 Hounsfield Units with respect to current proprietary state-of-the-art hybrid deep-learning/iterative method.