# Accelerating Atmospheric Turbulence Simulation via Learned Phase-to-Space Transform

arXiv: https://arxiv.org/abs/2107.11627 · HTML: https://mlsanity.com/paper/2107.11627/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 24 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image Reconstruction of Static and Dynamic Scenes through Anisoplanatic Turbulence](https://mlsanity.com/paper/2009.00071/) (2020)
- [Simulating Anisoplanatic Turbulence by Sampling Inter-modal and Spatially Correlated Zernike Coefficients](https://mlsanity.com/paper/2004.11210/) (2020)
- [Subsampled Turbulence Removal Network](https://mlsanity.com/paper/1807.04418/) (2018)
- [Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps](https://mlsanity.com/paper/1704.03140/) (2017)
- [Learning to Restore a Single Face Image Degraded by Atmospheric Turbulence using CNNs](https://mlsanity.com/paper/2007.08404/) (2020)

## Built on by (most cited first, 30 of 50)

- [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)
- [FarSight: A Physics-Driven Whole-Body Biometric System at Large Distance and Altitude](https://mlsanity.com/paper/2306.17206/) (2023)
- [Physics-Driven Turbulence Image Restoration with Stochastic Refinement](https://mlsanity.com/paper/2307.10603/) (2023)
- [Spatio-Temporal Turbulence Mitigation: A Translational Perspective](https://mlsanity.com/paper/2401.04244/) (2024)
- [LTT-GAN: Looking Through Turbulence by Inverting GANs](https://mlsanity.com/paper/2112.02379/) (2021)
- [Atmospheric Turbulence Removal with Complex-Valued Convolutional Neural Network](https://mlsanity.com/paper/2204.06989/) (2022)
- [Person Recognition at Altitude and Range: Fusion of Face, Body Shape and Gait](https://mlsanity.com/paper/2505.04616/) (2025)
- [TurbuGAN: An Adversarial Learning Approach to Spatially-Varying Multiframe Blind Deconvolution with Applications to Imaging Through Turbulence](https://mlsanity.com/paper/2203.06764/) (2022)
- [Deep Learning Techniques for Atmospheric Turbulence Removal: A Review](https://mlsanity.com/paper/2409.14587/) (2024)
- [Learning Phase Distortion with Selective State Space Models for Video Turbulence Mitigation](https://mlsanity.com/paper/2504.02697/) (2025)
- [Long-range Turbulence Mitigation: A Large-scale Dataset and A Coarse-to-fine Framework](https://mlsanity.com/paper/2407.08377/) (2024)
- [Atmospheric Turbulence Correction via Variational Deep Diffusion](https://mlsanity.com/paper/2305.05077/) (2023)
- [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)
- [DeTurb: Atmospheric Turbulence Mitigation with Deformable 3D Convolutions and 3D Swin Transformers](https://mlsanity.com/paper/2407.20855/) (2024)
- [MAMAT: 3D Mamba-Based Atmospheric Turbulence Removal and its Object Detection Capability](https://mlsanity.com/paper/2503.17700/) (2025)
- [Object recognition in atmospheric turbulence scenes](https://mlsanity.com/paper/2210.14318/) (2022)
- [Weakly Supervised Face and Whole Body Recognition in Turbulent Environments](https://mlsanity.com/paper/2308.11757/) (2023)
- [Real-World Atmospheric Turbulence Correction via Domain Adaptation](https://mlsanity.com/paper/2402.07371/) (2024)
- [A comparison of different atmospheric turbulence simulation methods for image restoration](https://mlsanity.com/paper/2204.08974/) (2022)
- [CATFace: Cross-Attribute-Guided Transformer with Self-Attention Distillation for Low-Quality Face Recognition](https://mlsanity.com/paper/2401.03037/) (2024)
- [NeRT: Implicit Neural Representations for General Unsupervised Turbulence Mitigation](https://mlsanity.com/paper/2308.00622/) (2023)
- [Source-free Domain Adaptation for Video Object Detection Under Adverse Image Conditions](https://mlsanity.com/paper/2404.15252/) (2024)
- [DMAT: An End-to-End Framework for Joint Atmospheric Turbulence Mitigation and Object Detection](https://mlsanity.com/paper/2507.04323/) (2025)
- [Are you In or Out (of gallery)? Wisdom from the Same-Identity Crowd](https://mlsanity.com/paper/2508.06357/) (2025)
- [SLCFormer: Spectral-Local Context Transformer with Physics-Grounded Flare Synthesis for Nighttime Flare Removal](https://mlsanity.com/paper/2512.15221/) (2025)
- [Thermal to Visible Image Synthesis under Atmospheric Turbulence](https://mlsanity.com/paper/2204.03057/) (2022)
- [Reconstructing Satellites in 3D from Amateur Telescope Images](https://mlsanity.com/paper/2404.18394/) (2024)

## Abstract (arXiv)

Fast and accurate simulation of imaging through atmospheric turbulence is essential for developing turbulence mitigation algorithms. Recognizing the limitations of previous approaches, we introduce a new concept known as the phase-to-space (P2S) transform to significantly speed up the simulation. P2S is build upon three ideas: (1) reformulating the spatially varying convolution as a set of invariant convolutions with basis functions, (2) learning the basis function via the known turbulence statistics models, (3) implementing the P2S transform via a light-weight network that directly convert the phase representation to spatial representation. The new simulator offers 300x -- 1000x speed up compared to the mainstream split-step simulators while preserving the essential turbulence statistics.