# Exploring the Low-Pass Filtering Behavior in Image Super-Resolution

arXiv: https://arxiv.org/abs/2405.07919 · HTML: https://mlsanity.com/paper/2405.07919/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Activating More Pixels in Image Super-Resolution Transformer](https://mlsanity.com/paper/2205.04437/) (2022)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Lightweight Image Super-Resolution with Information Multi-distillation Network](https://mlsanity.com/paper/1909.11856/) (2019)
- [Learning in the Frequency Domain](https://mlsanity.com/paper/2002.12416/) (2020)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Deep Learning for Single Image Super-Resolution: A Brief Review](https://mlsanity.com/paper/1808.03344/) (2018)
- [Efficient and Explicit Modelling of Image Hierarchies for Image Restoration](https://mlsanity.com/paper/2303.00748/) (2023)
- [Interpreting Super-Resolution Networks with Local Attribution Maps](https://mlsanity.com/paper/2011.11036/) (2020)
- [Local Texture Estimator for Implicit Representation Function](https://mlsanity.com/paper/2111.08918/) (2021)
- [Learning A Single Network for Scale-Arbitrary Super-Resolution](https://mlsanity.com/paper/2004.03791/) (2020)
- [Super-Resolution Neural Operator](https://mlsanity.com/paper/2303.02584/) (2023)
- [Implicit Transformer Network for Screen Content Image Continuous Super-Resolution](https://mlsanity.com/paper/2112.06174/) (2021)
- [Understanding training and generalization in deep learning by Fourier analysis](https://mlsanity.com/paper/1808.04295/) (2018)
- [Explicitizing an Implicit Bias of the Frequency Principle in Two-layer Neural Networks](https://mlsanity.com/paper/1905.10264/) (2019)
- [OPE-SR: Orthogonal Position Encoding for Designing a Parameter-free Upsampling Module in Arbitrary-scale Image Super-Resolution](https://mlsanity.com/paper/2303.01091/) (2023)

## Built on by (most cited first, 7 of 7)

- [From Zero to Detail: Deconstructing Ultra-High-Definition Image Restoration from Progressive Spectral Perspective](https://mlsanity.com/paper/2503.13165/) (2025)
- [LightGen: Efficient Image Generation through Knowledge Distillation and Direct Preference Optimization](https://mlsanity.com/paper/2503.08619/) (2025)
- [Temporal Regularization Makes Your Video Generator Stronger](https://mlsanity.com/paper/2503.15417/) (2025)
- [From Zero to Detail: A Progressive Spectral Decoupling Paradigm for UHD Image Restoration with New Benchmark](https://mlsanity.com/paper/2604.15654/) (2026)
- [MIGA: Mutual Information-Guided Attack on Denoising Models for Semantic Manipulation](https://mlsanity.com/paper/2503.06966/) (2025)
- [High-Resolution Magnetic Particle Imaging System Matrix Recovery Using a Vision Transformer with Residual Feature Network](https://mlsanity.com/paper/2511.02212/) (2025)
- [Revisiting Global Token Mixing in Task-Dependent MRI Restoration: Insights from Minimal Gated CNN Baselines](https://mlsanity.com/paper/2603.01449/) (2026)

## Abstract (arXiv)

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.