# Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz

arXiv: https://arxiv.org/abs/2305.07618 · HTML: https://mlsanity.com/paper/2305.07618/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 63 references that are in the map.
- First posted on arXiv 12 May 2023.

## Builds on (most cited first, 30 of 39)

- [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)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Compression Artifacts Reduction by a Deep Convolutional Network](https://mlsanity.com/paper/1504.06993/) (2015)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [On hallucinations in tomographic image reconstruction](https://mlsanity.com/paper/2012.00646/) (2020)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems](https://mlsanity.com/paper/2001.01258/) (2020)
- [A Benchmark of Medical Out of Distribution Detection](https://mlsanity.com/paper/2007.04250/) (2020)
- [Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networks](https://mlsanity.com/paper/2208.03160/) (2022)
- [On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regression](https://mlsanity.com/paper/2008.07281/) (2020)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [On Lipschitz Bounds of General Convolutional Neural Networks](https://mlsanity.com/paper/1808.01415/) (2018)
- [Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant](https://mlsanity.com/paper/2001.06263/) (2020)
- [Single Model Uncertainty Estimation via Stochastic Data Centering](https://mlsanity.com/paper/2207.07235/) (2022)
- [Compressible Latent-Space Invertible Networks for Generative Model-Constrained Image Reconstruction](https://mlsanity.com/paper/2007.02462/) (2020)
- [Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Prior](https://mlsanity.com/paper/2008.08837/) (2020)

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

- [The challenge of uncertainty quantification of large language models in medicine](https://mlsanity.com/paper/2504.05278/) (2025)
- [Exploring Out-of-distribution Detection for Sparse-view Computed Tomography with Diffusion Models](https://mlsanity.com/paper/2411.06308/) (2024)

## Abstract (arXiv)

Accurate image reconstruction is at the heart of diagnostics in medical imaging. Supervised deep learning-based approaches have been investigated for solving inverse problems including image reconstruction. However, these trained models encounter unseen data distributions that are widely shifted from training data during deployment. Therefore, it is essential to assess whether a given input falls within the training data distribution for diagnostic purposes. Uncertainty estimation approaches exist but focus on providing an uncertainty map to radiologists, rather than assessing the training distribution fit. In this work, we propose a method based on the local Lipschitz-based metric to distinguish out-of-distribution images from in-distribution with an area under the curve of 99.94%. Empirically, we demonstrate a very strong relationship between the local Lipschitz value and mean absolute error (MAE), supported by a high Spearman's rank correlation coefficient of 0.8475, which determines the uncertainty estimation threshold for optimal model performance. Through the identification of false positives, the local Lipschitz and MAE relationship was used to guide data augmentation and reduce model uncertainty. Our study was validated using the AUTOMAP architecture for sensor-to-image Magnetic Resonance Imaging (MRI) reconstruction. We compare our proposed approach with baseline methods: Monte-Carlo dropout and deep ensembles, and further analysis included MRI denoising and Computed Tomography (CT) sparse-to-full view reconstruction using UNET architectures. We show that our approach is applicable to various architectures and learned functions, especially in the realm of medical image reconstruction, where preserving the diagnostic accuracy of reconstructed images remains paramount.