# A Bayesian Based Deep Unrolling Algorithm for Single-Photon Lidar Systems

arXiv: https://arxiv.org/abs/2201.10910 · HTML: https://mlsanity.com/paper/2201.10910/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://mlsanity.com/paper/1502.03044/) (2015)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [SMD-Nets: Stereo Mixture Density Networks](https://mlsanity.com/paper/2104.03866/) (2021)
- [Efficient Image Super-Resolution Using Pixel Attention](https://mlsanity.com/paper/2010.01073/) (2020)
- [Real-time 3D reconstruction from single-photon lidar data using plug-and-play point cloud denoisers](https://mlsanity.com/paper/1905.06700/) (2019)
- [Robust super-resolution depth imaging via a multi-feature fusion deep network](https://mlsanity.com/paper/2011.11444/) (2020)
- [Bayesian 3D Reconstruction of Complex Scenes from Single-Photon Lidar Data](https://mlsanity.com/paper/1810.11633/) (2018)
- [Object Depth Profile and Reflectivity Restoration from Sparse Single-Photon Data Acquired in Underwater Environments](https://mlsanity.com/paper/1608.06143/) (2016)
- [Robust and Guided Bayesian Reconstruction of Single-Photon 3D Lidar Data: Application to Multispectral and Underwater Imaging](https://mlsanity.com/paper/2103.10122/) (2021)
- [Fast Task-Based Adaptive Sampling for 3D Single-Photon Multispectral Lidar Data](https://mlsanity.com/paper/2109.01743/) (2021)
- [Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover](https://mlsanity.com/paper/2110.10391/) (2021)

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

- [Interpretability of Machine Learning: Recent Advances and Future Prospects](https://mlsanity.com/paper/2305.00537/) (2023)
- [Graph Attention-Driven Bayesian Deep Unrolling for Dual-Peak Single-Photon Lidar Imaging](https://mlsanity.com/paper/2504.02480/) (2025)

## Abstract (arXiv)

Deploying 3D single-photon Lidar imaging in real world applications faces multiple challenges including imaging in high noise environments. Several algorithms have been proposed to address these issues based on statistical or learning-based frameworks. Statistical methods provide rich information about the inferred parameters but are limited by the assumed model correlation structures, while deep learning methods show state-of-the-art performance but limited inference guarantees, preventing their extended use in critical applications. This paper unrolls a statistical Bayesian algorithm into a new deep learning architecture for robust image reconstruction from single-photon Lidar data, i.e., the algorithm's iterative steps are converted into neural network layers. The resulting algorithm benefits from the advantages of both statistical and learning based frameworks, providing best estimates with improved network interpretability. Compared to existing learning-based solutions, the proposed architecture requires a reduced number of trainable parameters, is more robust to noise and mismodelling effects, and provides richer information about the estimates including uncertainty measures. Results on synthetic and real data show competitive results regarding the quality of the inference and computational complexity when compared to state-of-the-art algorithms.