Uncertainty Quantification for Deep Unrolling-Based Computational Imaging

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve state-of-the-art performance for imaging problems and allow the incorporation of the observation model into the reconstruction process, they do not provide any uncertainty information about the reconstructed image, which severely limits their use in practice, especially for safety-critical imaging applications. In this article, we propose a learning-based image reconstruction framework that incorporates the observation model into the reconstruction task and that is capable of quantifying epistemic and aleatoric uncertainties, based on deep unrolling and Bayesian neural networks. We demonstrate the uncertainty characterization capability of the proposed framework on magnetic resonance imaging and computed tomography reconstruction problems. We investigate the characteristics of the epistemic and aleatoric uncertainty information provided by the proposed framework to motivate future research on utilizing uncertainty information to develop more accurate, robust, trustworthy, uncertainty-aware, learning-based image reconstruction and analysis methods for imaging problems. We show that the proposed framework can provide uncertainty information while achieving comparable reconstruction performance to state-of-the-art deep unrolling methods.