# Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification

arXiv: https://arxiv.org/abs/1611.06345 · HTML: https://mlsanity.com/paper/1611.06345/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2016.

## Built on by (most cited first, 22 of 22)

- [Wave-ViT: Unifying Wavelet and Transformers for Visual Representation Learning](https://mlsanity.com/paper/2207.04978/) (2022)
- [Wave-SAN: Wavelet based Style Augmentation Network for Cross-Domain Few-Shot Learning](https://mlsanity.com/paper/2203.07656/) (2022)
- [Structure-Preserving Image Super-Resolution](https://mlsanity.com/paper/2109.12530/) (2021)
- [Stage-by-stage Wavelet Optimization Refinement Diffusion Model for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2308.15942/) (2023)
- [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)
- [Asymmetric CNN for image super-resolution](https://mlsanity.com/paper/2103.13634/) (2021)
- [TDA-Net: Fusion of Persistent Homology and Deep Learning Features for COVID-19 Detection in Chest X-Ray Images](https://mlsanity.com/paper/2101.08398/) (2021)
- [EWT: Efficient Wavelet-Transformer for Single Image Denoising](https://mlsanity.com/paper/2304.06274/) (2023)
- [Wavelet-Based Network For High Dynamic Range Imaging](https://mlsanity.com/paper/2108.01434/) (2021)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [Persistent Homology and Graphs Representation Learning](https://mlsanity.com/paper/2102.12926/) (2021)
- [Priors in Deep Image Restoration and Enhancement: A Survey](https://mlsanity.com/paper/2206.02070/) (2022)
- [WaveDH: Wavelet Sub-bands Guided ConvNet for Efficient Image Dehazing](https://mlsanity.com/paper/2404.01604/) (2024)
- [Finger-UNet: A U-Net based Multi-Task Architecture for Deep Fingerprint Enhancement](https://mlsanity.com/paper/2310.00629/) (2023)
- [Spectral U-Net: Enhancing Medical Image Segmentation via Spectral Decomposition](https://mlsanity.com/paper/2409.09216/) (2024)
- [Denoising single images by feature ensemble revisited](https://mlsanity.com/paper/2207.05176/) (2022)
- [Explaining the Power of Topological Data Analysis in Graph Machine Learning](https://mlsanity.com/paper/2401.04250/) (2024)
- [Adaptive Convolutional Neural Network for Image Super-resolution](https://mlsanity.com/paper/2402.15704/) (2024)
- [A Tree-guided CNN for image super-resolution](https://mlsanity.com/paper/2506.02585/) (2025)
- [Attention based Broadly Self-guided Network for Low light Image Enhancement](https://mlsanity.com/paper/2112.06226/) (2021)
- [Topology-enhanced machine learning for speech signal processing](https://mlsanity.com/paper/2311.15210/) (2023)
- [Wavelet-Enhanced Desnowing: A Novel Single Image Restoration Approach for Traffic Surveillance under Adverse Weather Conditions](https://mlsanity.com/paper/2503.01339/) (2025)

## Abstract (arXiv)

The latest deep learning approaches perform better than the state-of-the-art signal processing approaches in various image restoration tasks. However, if an image contains many patterns and structures, the performance of these CNNs is still inferior. To address this issue, here we propose a novel feature space deep residual learning algorithm that outperforms the existing residual learning. The main idea is originated from the observation that the performance of a learning algorithm can be improved if the input and/or label manifolds can be made topologically simpler by an analytic mapping to a feature space. Our extensive numerical studies using denoising experiments and NTIRE single-image super-resolution (SISR) competition demonstrate that the proposed feature space residual learning outperforms the existing state-of-the-art approaches. Moreover, our algorithm was ranked third in NTIRE competition with 5-10 times faster computational time compared to the top ranked teams. The source code is available on page : https://github.com/iorism/CNN.git