可逆残差网络在真实成像任务中表现优异，兼具理论保障与可解释性。
Invertible ResNets for Inverse Imaging Problems: Competitive Performance with Provable Regularization Properties
- 采用可逆残差网络构建可证明收敛的正则化重建方法
- 在模糊与非线性扩散任务中达到顶尖性能，训练耗时较长
- 具备内在稳定性与可逆性，提升鲁棒性与模型可解释性
基于学习的方法在求解逆问题方面表现出色，尤其在图像重建任务中。然而，这些方法通常缺乏理论保证，这在医学成像等敏感应用中尤为关键。Arndt 等人近期分析了基于可逆残差网络（iResNets）的数据驱动重建方法，发现其在合理假设下构成一个收敛的正则化方案。但此前仅在学术玩具问题和小规模 iResNet 上验证。本文通过在两个真实成像任务——线性模糊算子和非线性扩散算子上评估 iResNet 性能，将其与当前最先进的神经网络对比，结果表明其具有竞争力，但需更长训练时间。此外，我们数值验证了 iResNet 内在稳定性和可逆性的优势，展示了其在多种场景下的更强鲁棒性及对所学算子的可解释性，从而降低了重建方案的黑箱特性。
原文摘要 · Abstract (English)
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.
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