# Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames

arXiv: https://arxiv.org/abs/2504.13432 · HTML: https://mlsanity.com/paper/2504.13432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 24 of 24)

- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [DeblurGAN: Blind Motion Deblurring Using Conditional Adversarial Networks](https://mlsanity.com/paper/1711.07064/) (2017)
- [DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Better](https://mlsanity.com/paper/1908.03826/) (2019)
- [Learning to Discover Cross-Domain Relations with Generative Adversarial Networks](https://mlsanity.com/paper/1703.05192/) (2017)
- [Learning Correspondence from the Cycle-Consistency of Time](https://mlsanity.com/paper/1903.07593/) (2019)
- [Learning Dense Correspondence via 3D-guided Cycle Consistency](https://mlsanity.com/paper/1604.05383/) (2016)
- [MoCha-Stereo: Motif Channel Attention Network for Stereo Matching](https://mlsanity.com/paper/2404.06842/) (2024)
- [Image Reconstruction of Static and Dynamic Scenes through Anisoplanatic Turbulence](https://mlsanity.com/paper/2009.00071/) (2020)
- [Unsupervised Image Denoising in Real-World Scenarios via Self-Collaboration Parallel Generative Adversarial Branches](https://mlsanity.com/paper/2308.06776/) (2023)
- [Atmospheric Turbulence Removal with Complex-Valued Convolutional Neural Network](https://mlsanity.com/paper/2204.06989/) (2022)
- [Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps](https://mlsanity.com/paper/1704.03140/) (2017)
- [ATFaceGAN: Single Face Image Restoration and Recognition from Atmospheric Turbulence](https://mlsanity.com/paper/1910.03119/) (2019)
- [Landmark and Intensity Based Registration with Large Deformations via Quasi-conformal Maps](https://mlsanity.com/paper/1310.1710/) (2013)
- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [Fast Disk Conformal Parameterization of Simply-connected Open Surfaces](https://mlsanity.com/paper/1408.6974/) (2014)
- [Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing](https://mlsanity.com/paper/1508.07569/) (2015)
- [A Learning-based Framework for Topology-Preserving Segmentation using Quasiconformal Mappings](https://mlsanity.com/paper/2210.03299/) (2022)
- [Free-boundary conformal parameterization of point clouds](https://mlsanity.com/paper/2010.15399/) (2020)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [Re-boosting Self-Collaboration Parallel Prompt GAN for Unsupervised Image Restoration](https://mlsanity.com/paper/2408.09241/) (2024)
- [Diffeomorphic Template Registration for Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2405.03662/) (2024)
- [QIS : Interactive Segmentation via Quasi-Conformal Mappings](https://mlsanity.com/paper/2402.14695/) (2024)

## Abstract (arXiv)

Imaging through inhomogeneous media often results in severe distortions, posing significant challenges to downstream image-processing tasks. The lack of clean paired images makes supervised learning impractical, motivating unsupervised restoration approaches. In this work, we propose the Circular Quasi-Conformal Deturbulence (CQCD) framework, an unsupervised approach that reconstructs distortion-free images from multiple frames using a circular architecture. The framework minimizes reconstruction errors by jointly estimating forward and backward transformations between distorted observations and the restored image. A key advancement of CQCD is the integration of computational quasi-conformal geometry, which encourages bijective non-rigid deformations and improves the well-posedness of both forward and inverse mappings for cycle consistency. The deformation field is further regularized to preserve structural coherence and reduce non-physical artifacts such as folding or tearing. Additionally, tight-frame blocks are employed to effectively encode distortion-sensitive features, enhancing the precision of the restoration process. To assess the effectiveness of the proposed framework, extensive evaluations are conducted on synthetic and real-world image datasets. Experimental findings indicate that CQCD not only surpasses existing state-of-the-art deturbulence techniques in restoration quality but also achieves highly accurate deformation field estimation.