A Plug-and-Play Method with Inpainting Network for Bayesian Uncertainty Quantification in Imaging

Source abstract

Abstract We contribute to an uncertainty quantification problem in imaging that evaluates a hypothesis test questioning the existence of local “artifacts” appearing in the maximum a posteriori (MAP) estimate (obtained from standard numerical tools). Such a method, called Bayesian uncertainty quantification by optimization (BUQO), was introduced a few years ago as an efficient and scalable alternative to sampling methods when per-pixel error bars are not needed. BUQO formulates a hypothesis test for probing the existence of local structures in the MAP estimate as a minimization problem that can be solved efficiently with standard optimization algorithms. In this context, BUQO requires a “mathematical” definition of the “local artifact.” This definition can be interpreted as an inpainting of the structure. However, only simple handcrafted techniques have been proposed so far due to the complexity of the problem. In this work, we propose a data-driven alternative to BUQO where the inpainting procedure in the algorithm is performed using a convolutional inpainting neural network (NN). This results in a plug-and-play algorithm, based on the primal-dual Condat–Vũ iterations, where the inpainting procedure is performed with a NN. The proposed approach is assessed on two image reconstruction problems inspired by medicine. We specifically perform simulations on two Fourier undersampling problems (discrete and non-uniform) encountered in magnetic resonance imaging, as well as a computed tomography problem using the Radon measurement operator.