  Uncertainty quantification in image restoration is a prominent challenge,
mainly due to the high dimensionality of the encountered problems. Recently, a
Bayesian uncertainty quantification by optimization (BUQO) has been proposed to
formulate hypothesis testing as a minimization problem. The objective is to
determine whether a structure appearing in a maximum a posteriori estimate is
true or is a reconstruction artifact due to the ill-posedness or
ill-conditioness of the problem. In this context, the mathematical definition
of having a ``fake structure" is crucial, and highly depends on the type of
structure of interest. This definition can be interpreted as an inpainting of a
neighborhood of the structure, but only simple techniques have been proposed in
the literature so far, due to the complexity of the problem. In this work, we
propose a data-driven method using a simple convolutional neural network to
perform the inpainting task, leading to a novel plug-and-play BUQO algorithm.
Compared to previous works, the proposed approach has the advantage that it can
be used for a wide class of structures, without needing to adapt the inpainting
operator to the area of interest. In addition, we show through simulations on
magnetic resonance imaging, that compared to the original BUQO's hand-crafted
inpainting procedure, the proposed approach provides greater qualitative output
images. Python code will be made available for reproducibility upon acceptance
of the article.
