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：用于图像超分辨率（ISR）的深度神经网络相较于插值等传统方法已展现出显著优势。然而，与具有坚实数学基础的传统方法相比，它们常被批评为"黑箱"。本文尝试利用信号处理领域的理论来解释深度神经网络在ISR中的行为。首先，我们报告了一个被称为"辛格现象"的有趣现象，该现象在向神经网络馈入脉冲输入时出现。基于此观察，我们提出了一种名为混合响应分析（HyRA）的方法，用于分析神经网络在ISR任务中的行为。具体而言，HyRA将神经网络分解为一个线性系统与一个非线性系统的并联连接，并证明线性系统充当低通滤波器，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，我们引入了一种用于图像到图像任务的度量标准，称为频谱分布相似度（FSDS）。FSDS反映了不同频率分量的分布相似性，能够捕捉传统度量标准可能忽略的细微差别。本文的代码、视频及原始实验结果可见于：https://github.com/RisingEntropy/LPFInISR。