# Variational Deep Unfolding with Mamba-Based Nonlocal Modeling for Underwater Image Enhancement

arXiv: https://arxiv.org/abs/2606.14781 · HTML: https://mlsanity.com/paper/2606.14781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mamba for image restoration, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## 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, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [An Underwater Image Enhancement Benchmark Dataset and Beyond](https://mlsanity.com/paper/1901.05495/) (2019)
- [Underwater Image Enhancement via Medium Transmission-Guided Multi-Color Space Embedding](https://mlsanity.com/paper/2104.13015/) (2021)
- [WaterGAN: Unsupervised Generative Network to Enable Real-time Color Correction of Monocular Underwater Images](https://mlsanity.com/paper/1702.07392/) (2017)
- [Enhancing Underwater Imagery using Generative Adversarial Networks](https://mlsanity.com/paper/1801.04011/) (2018)
- [Shallow-UWnet : Compressed Model for Underwater Image Enhancement](https://mlsanity.com/paper/2101.02073/) (2021)
- [UIEC^2-Net: CNN-based Underwater Image Enhancement Using Two Color Space](https://mlsanity.com/paper/2103.07138/) (2021)
- [SGUIE-Net: Semantic Attention Guided Underwater Image Enhancement with Multi-Scale Perception](https://mlsanity.com/paper/2201.02832/) (2022)
- [Phaseformer: Phase-based Attention Mechanism for Underwater Image Restoration and Beyond](https://mlsanity.com/paper/2412.01456/) (2024)
- [Underwater Image Restoration via Polymorphic Large Kernel CNNs](https://mlsanity.com/paper/2412.18459/) (2024)
- [On the Duality Between Retinex and Image Dehazing](https://mlsanity.com/paper/1712.02754/) (2017)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [RAUNE-Net: A Residual and Attention-Driven Underwater Image Enhancement Method](https://mlsanity.com/paper/2311.00246/) (2023)
- [Mamba-UIE: Enhancing Underwater Images with Physical Model Constraint](https://mlsanity.com/paper/2407.19248/) (2024)
- [Dual High-Order Total Variation Model for Underwater Image Restoration](https://mlsanity.com/paper/2407.14868/) (2024)
- [UIE-UnFold: Deep Unfolding Network with Color Priors and Vision Transformer for Underwater Image Enhancement](https://mlsanity.com/paper/2408.10653/) (2024)
- [Nonlocal Retinex-Based Variational Model and its Deep Unfolding Twin for Low-Light Image Enhancement](https://mlsanity.com/paper/2504.07810/) (2025)

## Abstract (arXiv)

Underwater imaging plays a crucial role in ocean engineering, although captured data often suffer from poor visibility and color distortion. To address these challenges, we propose a model-based deep unfolding network for underwater image enhancement that integrates variational modeling into a learnable architecture. The framework is guided by a variational formulation based on a dehazing decomposition, incorporating a multiplicative residual component to absorb remaining artifacts and a nonlocal gradient-type constraint to preserve structural details and enhance edge sharpness. We provide a theoretical analysis establishing the existence of solution for the associated minimization problem. The proposed unfolding method incorporates Mamba layers to efficiently capture self-similarities in the scene. In addition, we introduce a proximal trajectory loss that enforces consistency between the unfolding stages and the iterations of an ideal restoration regularizer. Experimental results demonstrate that the proposed unfolding approach achieves improved visual quality and competitive quantitative performance compared with recent state-of-the-art methods. The source code will be available at https://github.com/MIA-UIB/Variational-Unfolding-Mamba-Underwater-Enhancement .