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

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. Current uncertainty estimation approaches 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 metric to distinguish out-of-distribution images from in-distribution with an area under the curve of 99.94% for True Positive Rate versus False Positive Rate. We demonstrate a very strong relationship between the local Lipschitz value and mean absolute error (MAE), supported by a Spearman's rank correlation coefficient of 0.8475, to determine an uncertainty estimation threshold for optimal performance. Through the identification of false positives, we demonstrate the local Lipschitz and MAE relationship can guide data augmentation and reduce uncertainty. Our study was validated using the AUTOMAP architecture for sensor-to-image Magnetic Resonance Imaging (MRI) reconstruction. We demonstrate our approach outperforms baseline techniques of Monte-Carlo dropout and deep ensembles as well as the state-of-the-art Mean Variance Estimation (MVE) network approach. We expand our application scope to MRI denoising and Computed Tomography (CT) sparse-to-full view reconstructions using UNET architectures. We show our approach is applicable to various architectures and applications, especially in medical imaging, where preserving diagnostic accuracy of reconstructed images remains paramount.