Model-Based Bayesian Deep Learning Architecture for Linear Inverse Problems in Computational Imaging

Abstract

We propose a neural network architecture combined with specific training and inference procedures for linear inverse problems arising in computational imaging to reconstruct the underlying image and to represent the uncertainty about the reconstruction. The proposed architecture is built from the model-based reconstruction perspective, which enforces data consistency and eliminates the artifacts in an alternating manner. The training and the inference procedures are based on performing approximate Bayesian analysis on the weights of the proposed network using a variational inference method. The proposed architecture with the associated inference procedure is capable of characterizing uncertainty while performing reconstruction with a modelbased approach. We tested the proposed method on a simulated magnetic resonance imaging experiment. We showed that the proposed method achieved an adequate reconstruction capability and provided reliable uncertainty estimates in the sense that the regions having high uncertainty provided by the proposed method are likely to be the regions where reconstruction errors occur.