# Learning Phase Distortion with Selective State Space Models for Video Turbulence Mitigation

arXiv: https://arxiv.org/abs/2504.02697 · HTML: https://mlsanity.com/paper/2504.02697/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Mamba for image restoration, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 55 of its 105 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Mamba for image restoration](https://mlsanity.com/ssm/mamba-for-image-restoration/)

## Builds on (most cited first, 30 of 55)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [An End-to-End Trainable Neural Network for Image-based Sequence Recognition and Its Application to Scene Text Recognition](https://mlsanity.com/paper/1507.05717/) (2015)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [VideoMamba: State Space Model for Efficient Video Understanding](https://mlsanity.com/paper/2403.06977/) (2024)
- [VRT: A Video Restoration Transformer](https://mlsanity.com/paper/2201.12288/) (2022)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Recurrent Video Restoration Transformer with Guided Deformable Attention](https://mlsanity.com/paper/2206.02146/) (2022)
- [Decoupled Attention Network for Text Recognition](https://mlsanity.com/paper/1912.10205/) (2019)
- [ZigMa: A DiT-style Zigzag Mamba Diffusion Model](https://mlsanity.com/paper/2403.13802/) (2024)
- [Spatially-Adaptive Image Restoration using Distortion-Guided Networks](https://mlsanity.com/paper/2108.08617/) (2021)
- [Expanding Accurate Person Recognition to New Altitudes and Ranges: The BRIAR Dataset](https://mlsanity.com/paper/2211.01917/) (2022)
- [MiM-ISTD: Mamba-in-Mamba for Efficient Infrared Small Target Detection](https://mlsanity.com/paper/2403.02148/) (2024)
- [FreqMamba: Viewing Mamba from a Frequency Perspective for Image Deraining](https://mlsanity.com/paper/2404.09476/) (2024)
- [RainMamba: Enhanced Locality Learning with State Space Models for Video Deraining](https://mlsanity.com/paper/2407.21773/) (2024)
- [Accelerating Atmospheric Turbulence Simulation via Learned Phase-to-Space Transform](https://mlsanity.com/paper/2107.11627/) (2021)
- [A Survey on Visual Mamba](https://mlsanity.com/paper/2404.15956/) (2024)
- [Wave-Mamba: Wavelet State Space Model for Ultra-High-Definition Low-Light Image Enhancement](https://mlsanity.com/paper/2408.01276/) (2024)
- [Single Frame Atmospheric Turbulence Mitigation: A Benchmark Study and A New Physics-Inspired Transformer Model](https://mlsanity.com/paper/2207.10040/) (2022)
- [Learning Degradation Representations for Image Deblurring](https://mlsanity.com/paper/2208.05244/) (2022)
- [AT-DDPM: Restoring Faces degraded by Atmospheric Turbulence using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2208.11284/) (2022)

## Built on by (most cited first, 9 of 9)

- [RMFAT: Recurrent Multi-scale Feature Atmospheric Turbulence Mitigator](https://mlsanity.com/paper/2508.11409/) (2025)
- [HATIR: Heat-Aware Diffusion for Turbulent Infrared Video Super-Resolution](https://mlsanity.com/paper/2601.04682/) (2026)
- [Continuous Exposure-Time Modeling for Realistic Atmospheric Turbulence Synthesis](https://mlsanity.com/paper/2603.01398/) (2026)
- [High-speed Imaging through Turbulence with Event-based Light Fields](https://mlsanity.com/paper/2603.14023/) (2026)
- [High-Quality and Efficient Turbulence Mitigation with Events](https://mlsanity.com/paper/2603.20708/) (2026)
- [A unified Benchmark for Multi-Frame Image Restoration under Severe Refractive Warping](https://mlsanity.com/paper/2605.05079/) (2026)
- [ReMATF: Recurrent Motion-Adaptive Multi-scale Turbulence Mitigation for Dynamic Scenes](https://mlsanity.com/paper/2605.21440/) (2026)
- [Restore What Matters: Lessons from Joint Restoration and Recognition](https://mlsanity.com/paper/2609.13791/) (2026)
- [ASTRA-SR: Atmospheric Seeing and Turbulence Restoration for Astronomical Image Super-Resolution](https://mlsanity.com/paper/2609.26731/) (2026)

## Abstract (arXiv)

Atmospheric turbulence is a major source of image degradation in long-range imaging systems. Although numerous deep learning-based turbulence mitigation (TM) methods have been proposed, many are slow, memory-hungry, and do not generalize well. In the spatial domain, methods based on convolutional operators have a limited receptive field, so they cannot handle a large spatial dependency required by turbulence. In the temporal domain, methods relying on self-attention can, in theory, leverage the lucky effects of turbulence, but their quadratic complexity makes it difficult to scale to many frames. Traditional recurrent aggregation methods face parallelization challenges. In this paper, we present a new TM method based on two concepts: (1) A turbulence mitigation network based on the Selective State Space Model (MambaTM). MambaTM provides a global receptive field in each layer across spatial and temporal dimensions while maintaining linear computational complexity. (2) Learned Latent Phase Distortion (LPD). LPD guides the state space model. Unlike classical Zernike-based representations of phase distortion, the new LPD map uniquely captures the actual effects of turbulence, significantly improving the model's capability to estimate degradation by reducing the ill-posedness. Our proposed method exceeds current state-of-the-art networks on various synthetic and real-world TM benchmarks with significantly faster inference speed.