# Deep-learning-driven Reliable Single-pixel Imaging with Uncertainty Approximation

arXiv: https://arxiv.org/abs/2107.11678 · HTML: https://mlsanity.com/paper/2107.11678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 24 Jul 2021.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [How to Start Training: The Effect of Initialization and Architecture](https://mlsanity.com/paper/1803.01719/) (2018)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [Reliable deep-learning-based phase imaging with uncertainty quantification](https://mlsanity.com/paper/1901.02038/) (2019)
- [Low Photon Count Phase Retrieval Using Deep Learning](https://mlsanity.com/paper/1806.10029/) (2018)
- [Deep speckle correlation: a deep learning approach towards scalable imaging through scattering media](https://mlsanity.com/paper/1806.04139/) (2018)
- [Deep Learning Microscopy](https://mlsanity.com/paper/1705.04709/) (2017)
- [High-Resolution Limited-Angle Phase Tomography of Dense Layered Objects Using Deep Neural Networks](https://mlsanity.com/paper/1812.07380/) (2018)
- [Optical machine learning with incoherent light and a single-pixel detector](https://mlsanity.com/paper/1904.10851/) (2019)
- [Computational ghost imaging using deep learning](https://mlsanity.com/paper/1710.08343/) (2017)
- [Review on Optical Image Hiding and Watermarking Techniques](https://mlsanity.com/paper/1804.05483/) (2018)

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

- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging](https://mlsanity.com/paper/2504.07696/) (2025)

## Abstract (arXiv)

Single-pixel imaging (SPI) has the advantages of high-speed acquisition over a broad wavelength range and system compactness, which are difficult to achieve by conventional imaging sensors. However, a common challenge is low image quality arising from undersampling. Deep learning (DL) is an emerging and powerful tool in computational imaging for many applications and researchers have applied DL in SPI to achieve higher image quality than conventional reconstruction approaches. One outstanding challenge, however, is that the accuracy of DL predictions in SPI cannot be assessed in practical applications where the ground truths are unknown. Here, we propose the use of the Bayesian convolutional neural network (BCNN) to approximate the uncertainty (coming from finite training data and network model) of the DL predictions in SPI. Each pixel in the predicted result from BCNN represents the parameter of a probability distribution rather than the image intensity value. Then, the uncertainty can be approximated with BCNN by minimizing a negative log-likelihood loss function in the training stage and Monte Carlo dropout in the prediction stage. The results show that the BCNN can reliably approximate the uncertainty of the DL predictions in SPI with varying compression ratios and noise levels. The predicted uncertainty from BCNN in SPI reveals that most of the reconstruction errors in deep-learning-based SPI come from the edges of the image features. The results show that the proposed BCNN can provide a reliable tool to approximate the uncertainty of DL predictions in SPI and can be widely used in many applications of SPI.