Deep neural networks for image super-resolution (ISR) have shown significant advantages over traditional approaches like the interpolation. However, they are often criticized as 'black boxes' compared to traditional approaches with solid mathematical foundations. In this paper, we attempt to interpret the behavior of deep neural networks in ISR using theories from the field of signal processing. First, we report an intriguing phenomenon, referred to as `the sinc phenomenon.' It occurs when an impulse input is fed to a neural network. Then, building on this observation, we propose a method named Hybrid Response Analysis (HyRA) to analyze the behavior of neural networks in ISR tasks. Specifically, HyRA decomposes a neural network into a parallel connection of a linear system and a non-linear system and demonstrates that the linear system functions as a low-pass filter while the non-linear system injects high-frequency information. Finally, to quantify the injected high-frequency information, we introduce a metric for image-to-image tasks called Frequency Spectrum Distribution Similarity (FSDS). FSDS reflects the distribution similarity of different frequency components and can capture nuances that traditional metrics may overlook. Code, videos and raw experimental results for this paper can be found in: https://github.com/RisingEntropy/LPFInISR.

翻译：针对图像超分辨率（ISR）的深度神经网络相较于插值等传统方法展现出显著优势，但这些方法常因缺乏传统方法所具备的坚实数学基础而被批评为“黑箱”。本文尝试利用信号处理领域的理论解释ISR中深度神经网络的行为。首先，我们报告一个被称为“sinc现象”的有趣现象——当向神经网络输入脉冲信号时会出现该现象。基于这一发现，我们提出名为混合响应分析（HyRA）的方法来分析ISR任务中神经网络的行为。具体而言，HyRA将神经网络分解为线性系统与非线性系统的并联结构，并论证线性系统发挥低通滤波器作用，而非线性系统则注入高频信息。最后，为量化注入的高频信息，我们引入面向图像到图像任务的度量指标——频谱分布相似度（FSDS）。FSDS反映不同频率分量的分布相似性，可捕捉传统度量指标可能忽略的细微差异。本文代码、视频及原始实验结果参见：https://github.com/RisingEntropy/LPFInISR