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.

翻译：图像恢复中的不确定性量化是一项突出挑战，主要源于所遇问题的高维度特性。近年来，一种通过优化进行贝叶斯不确定性量化（BUQO）的方法被提出，将假设检验表述为一个最小化问题。其目标在于判断最大后验估计中出现的结构是真实存在的，还是因问题的不适定性或病态条件而产生的重建伪影。在此背景下，“虚假结构”的数学定义至关重要，且高度依赖于所关注结构的类型。该定义可被解释为对结构邻域进行图像修补，但受限于问题复杂性，文献中目前仅提出了简单技术。本研究提出一种数据驱动方法，利用简单卷积神经网络执行图像修补任务，进而形成新型即插即用BUQO算法。与先前工作相比，所提方法的优势在于能够适用于广泛的结构类别，无需根据感兴趣区域调整修补算子。此外，我们通过磁共振成像模拟表明，与原始BUQO手工设计的修补流程相比，所提方法能提供更优质的定性输出图像。文章接收后，将公开Python代码以确保可复现性。