Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in sensitive applications such as medical imaging. Recent works by Arndt et al addressed this gap by analyzing a data-driven reconstruction method based on invertible residual networks (iResNets). They revealed that, under reasonable assumptions, this approach constitutes a convergent regularization scheme. However, the performance of the reconstruction method was only validated on academic toy problems and small-scale iResNet architectures. In this work, we address this gap by evaluating the performance of iResNets on two real-world imaging tasks: a linear blurring operator and a nonlinear diffusion operator. To do so, we compare the performance of iResNets against state-of-the-art neural networks, revealing their competitiveness at the expense of longer training times. Moreover, we numerically demonstrate the advantages of the iResNet's inherent stability and invertibility by showcasing increased robustness across various scenarios as well as interpretability of the learned operator, thereby reducing the black-box nature of the reconstruction scheme.

翻译：基于学习的方法在解决逆问题，特别是图像重建任务中展现了卓越的性能。尽管这些方法取得了成功，但它们通常缺乏理论保证，而这在医学成像等敏感应用中至关重要。Arndt等人的近期研究通过分析基于可逆残差网络（iResNets）的数据驱动重建方法填补了这一空白。他们揭示出，在合理假设下，该方法构成了一个收敛的正则化方案。然而，该重建方法的性能仅在学术性玩具问题和小规模iResNet架构上得到了验证。在本工作中，我们通过评估iResNets在两个真实世界成像任务上的性能来填补这一空白：线性模糊算子和非线性扩散算子。为此，我们将iResNets的性能与最先进的神经网络进行比较，揭示了其以更长的训练时间为代价所具备的竞争力。此外，我们通过展示其在多种场景下增强的鲁棒性以及所学算子的可解释性，数值化地证明了iResNet固有稳定性和可逆性的优势，从而减少了重建方案的黑箱特性。