The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies the noise on the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between neural networks stability and accuracy in the solution of linear inverse problems. Moreover, we propose different supervised and unsupervised solutions to increase network stability that maintains good accuracy by inheriting, in the network training, regularization from a model-based iterative scheme. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based solutions to stably solve noisy inverse problems.

翻译：例如,在信号和图像处理中出现的线性反问题的解决办法是一个具有挑战性的问题,因为不整齐地放大了数据上的噪音。最近引入了基于更传统的模型方法的深层次学习的算法,但通常在数据扰动方面受到不稳定的影响。在本文件中,我们从理论上分析了神经网络稳定性和准确性之间的权衡,以解决线性反面问题。此外,我们提出了不同的有监督的和不受监督的解决方案,以提高网络稳定性,保持良好的准确性,在网络培训中继承基于模型的迭接机制的正规化。关于图像模糊化的广泛数字实验证实了理论结果和拟议的深层次学习解决方案的有效性,这些解决方案旨在刺探解决吵闹的反面问题。