In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem, when trained end-to-end. In this paper, we propose some strategies to improve stability without losing to much accuracy to deblur images with deep-learning based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following, neural network-based, step. Two different pre-processors are presented: the former implements a strong parameter-free denoiser, and the latter is a variational model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.

翻译：近年来，大型卷积神经网络因其高精度图像复原能力而被广泛用于图像去模糊工具。众所周知，图像去模糊在数学上被建模为不适定反问题，当噪声影响数据时，其解难以近似。神经网络用于去模糊的一个局限性在于其对噪声及其他扰动的敏感性，这可能导致不稳定性并产生低质量重建。此外，端到端训练的神经网络未必能考虑底层成像问题的数值公式化表达。本文提出若干策略，在不显著损失精度的前提下，通过基于深度学习的方法提升图像去模糊的稳定性。首先，我们设计了一种极小的神经架构，在满足绿色人工智能需求的同时缩短训练执行时间，且不会在计算图像中过度放大噪声。其次，我们引入统一框架，通过预处理步骤平衡后续基于神经网络的步骤所缺乏的稳定性。文中提出两种不同的预处理器：前者实现了一种无需参数控制的强去噪器，后者则是基于变分模型的隐式成像问题正则化公式表达。该框架还通过数学分析进行了形式化表征。通过数值实验验证了所提方法在未知或未量化噪声存在时对图像去模糊的准确性与稳定性；结果表明，这些方法提升了网络对噪声的鲁棒性。特别地，基于模型的框架在视觉精度与稳健性之间实现了最可靠的权衡。