What Does Your Computational Imaging Algorithm Not Know?: A Plug-and-Play Model Quantifying Model Uncertainty

Canberk Ekmekci, Mujdat Cetin; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2021, pp. 4018-4027

Plug-and-Play is an algorithmic framework developed to solve image recovery problems. Thanks to the empirical success of convolutional neural network (CNN) denoisers, numerous Plug-and-Play algorithms utilizing CNN denoisers have been proposed to solve various image recovery tasks. Unfortunately, those Plug-and-Play algorithms lack representing the uncertainty on the parameters of CNN denoisers because their training procedure yields only a point estimate for the parameters of the CNN denoiser. In this paper, we present a novel Plug-and-Play model that quantifies the uncertainty on the parameters of the CNN denoiser. The proposed model places a probability distribution on the parameters of the CNN denoiser and carries out approximate Bayesian inference to obtain the posterior distribution of the parameters to characterize their uncertainty. The uncertainty information provided by the proposed Plug-and-Play model allows characterizing how certain the model is for a given input. The proposed Plug-and-Play model is applicable to a broad set of computational imaging problems, with the requirement that the data fidelity term is differentiable, and has a simple implementation in deep learning frameworks. We evaluate the proposed Plug-and-Play model on a magnetic resonance imaging reconstruction problem and demonstrate its uncertainty characterization capability.