  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.
