# Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps

arXiv: https://arxiv.org/abs/1704.03140 · HTML: https://mlsanity.com/paper/1704.03140/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2017.

## Built on by (most cited first, 18 of 18)

- [Accelerating Atmospheric Turbulence Simulation via Learned Phase-to-Space Transform](https://mlsanity.com/paper/2107.11627/) (2021)
- [Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Model](https://mlsanity.com/paper/2207.10040/) (2022)
- [AT-DDPM: Restoring Faces degraded by Atmospheric Turbulence using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2208.11284/) (2022)
- [Imaging through the Atmosphere using Turbulence Mitigation Transformer](https://mlsanity.com/paper/2207.06465/) (2022)
- [Physics-Driven Turbulence Image Restoration with Stochastic Refinement](https://mlsanity.com/paper/2307.10603/) (2023)
- [Learning to restore images degraded by atmospheric turbulence using uncertainty](https://mlsanity.com/paper/2207.03447/) (2022)
- [Spatio-Temporal Turbulence Mitigation: A Translational Perspective](https://mlsanity.com/paper/2401.04244/) (2024)
- [Learning Phase Distortion with Selective State Space Models for Video Turbulence Mitigation](https://mlsanity.com/paper/2504.02697/) (2025)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [Long-range Turbulence Mitigation: A Large-scale Dataset and A Coarse-to-fine Framework](https://mlsanity.com/paper/2407.08377/) (2024)
- [Turb-Seg-Res: A Segment-then-Restore Pipeline for Dynamic Videos with Atmospheric Turbulence](https://mlsanity.com/paper/2404.13605/) (2024)
- [Diffeomorphic Template Registration for Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2405.03662/) (2024)
- [Weakly Supervised Face and Whole Body Recognition in Turbulent Environments](https://mlsanity.com/paper/2308.11757/) (2023)
- [A comparison of different atmospheric turbulence simulation methods for image restoration](https://mlsanity.com/paper/2204.08974/) (2022)
- [Rethinking Point Cloud Filtering: A Non-Local Position Based Approach](https://mlsanity.com/paper/2110.07253/) (2021)
- [Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis](https://mlsanity.com/paper/2603.01398/) (2026)
- [Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames](https://mlsanity.com/paper/2504.13432/) (2025)
- [GSTurb: Gaussian Splatting for Atmospheric Turbulence Mitigation](https://mlsanity.com/paper/2602.22800/) (2026)

## Abstract (arXiv)

We address the problem of restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. A novel algorithm is proposed in this paper to reduce geometric distortion as well as space-and-time-varying blur due to strong turbulence. By considering a suitable energy functional, our algorithm first obtains a sharp reference image and a subsampled image sequence containing sharp and mildly distorted image frames with respect to the reference image. The subsampled image sequence is then stabilized by applying the Robust Principal Component Analysis (RPCA) on the deformation fields between image frames and warping the image frames by a quasiconformal map associated with the low-rank part of the deformation matrix. After image frames are registered to the reference image, the low-rank part of them are deblurred via a blind deconvolution, and the deblurred frames are then fused with the enhanced sparse part. Experiments have been carried out on both synthetic and real turbulence-distorted video. Results demonstrate that our method is effective in alleviating distortions and blur, restoring image details and enhancing visual quality.