用数学工具提升图像重建稳定性，让旧模型更可靠。
Stabilizing RED using the Koopman Operator
- 用柯普曼算子分析重建过程动态，捕捉局部行为
- 通过谱半径判断不稳，自动调节步长避免发散
- 无需重训、通用性强，适合各类预训练去噪器
广泛使用的RED（正则化去噪）框架利用预训练去噪器作为隐式正则项进行模型化重建。尽管RED通常能生成高保真结果，但黑箱去噪器有时会导致不稳定性。本文提出一种数据驱动的机制，使用柯普曼算子这一经典动力系统分析工具来稳定RED。具体地，我们用该算子在低维特征空间中捕获RED的局部动态，其谱半径用于检测不稳定性，并制定一种模型无关的自适应步长规则，计算开销小，无需重训练。我们在多个预训练去噪器上验证了所提柯普曼稳定方法的有效性。
原文摘要 · Abstract (English)
The widely used RED (Regularization-by-Denoising) framework uses pretrained denoisers as implicit regularizers for model-based reconstruction. Although RED generally yields high-fidelity reconstructions, the use of black-box denoisers can sometimes lead to instability. In this letter, we propose a data-driven mechanism to stabilize RED using the Koopman operator, a classical tool for analyzing dynamical systems. Specifically, we use the operator to capture the local dynamics of RED in a low-dimensional feature space, and its spectral radius is used to detect instability and formulate an adaptive step-size rule that is model-agnostic, has modest overhead, and requires no retraining. We test this with several pretrained denoisers to demonstrate the effectiveness of the proposed Koopman stabilization.
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