Conformalized Generative Bayesian Imaging: An Uncertainty Quantification Framework for Computational Imaging

Uncertainty quantification plays an important role in achieving trustworthy and reliable learning-based computational imaging. Recent advances in generative modeling and Bayesian neural networks have enabled the development of uncertainty-aware image reconstruction methods. Current generative model-based methods seek to quantify the inherent (aleatoric) uncertainty on the underlying image for given measurements by learning to sample from the posterior distribution of the underlying image. On the other hand, Bayesian neural network-based approaches aim to quantify the model (epistemic) uncertainty on the parameters of a deep neural network-based reconstruction method by approximating the posterior distribution of those parameters. Unfortunately, an ongoing need for an inversion method that can jointly quantify complex aleatoric uncertainty and epistemic uncertainty patterns still persists. In this paper, we present a scalable framework that can quantify both aleatoric and epistemic uncertainties. The proposed framework accepts an existing generative model-based posterior sampling method as an input and introduces an epistemic uncertainty quantification capability through Bayesian neural networks with latent variables and deep ensembling. Furthermore, by leveraging the conformal prediction methodology, the proposed framework can be easily calibrated to ensure rigorous uncertainty quantification. We evaluated the proposed framework on magnetic resonance imaging, computed tomography, and image inpainting problems and showed that the epistemic and aleatoric uncertainty estimates produced by the proposed framework display the characteristic features of true epistemic and aleatoric uncertainties. Furthermore, our results demonstrated that the use of conformal prediction on top of the proposed framework enables marginal coverage guarantees consistent with frequentist principles.

Integrating Generative and Physics-Based Models for Ptychographic Imaging with Uncertainty Quantification

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant amount of overlap between adjacent scan locations, leading to large data volumes and prolonged acquisition times. To address this key limitation, this paper proposes a Bayesian inversion method for ptychography that performs effectively even with less overlap between neighboring scan locations. Furthermore, the proposed method can quantify the inherent uncertainty on the ptychographic object, which is created by the ill-posed nature of the ptychographic inverse problem. At a high level, the proposed method first utilizes a deep generative model to learn the prior distribution of the object and then generates samples from the posterior distribution of the object by using a Markov Chain Monte Carlo algorithm. Our results from simulated ptychography experiments show that the proposed framework can consistently outperform a widely used iterative reconstruction algorithm in cases of reduced overlap. Moreover, the proposed framework can provide uncertainty estimates that closely correlate with the true error, which is not available in practice. The project website is available here.

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 paper, 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.