# First-order State Space Model for Lightweight Image Super-resolution

arXiv: https://arxiv.org/abs/2509.08458 · HTML: https://mlsanity.com/paper/2509.08458/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Vision Mamba backbones, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Vision Mamba backbones](https://mlsanity.com/ssm/vision-mamba-backbones/)

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

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Activating More Pixels in Image Super-Resolution Transformer](https://mlsanity.com/paper/2205.04437/) (2022)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Sketch-based Manga Retrieval using Manga109 Dataset](https://mlsanity.com/paper/1510.04389/) (2015)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Neighborhood Attention Transformer](https://mlsanity.com/paper/2204.07143/) (2022)
- [Lightweight Image Super-Resolution with Information Multi-distillation Network](https://mlsanity.com/paper/1909.11856/) (2019)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [LAPAR: Linearly-Assembled Pixel-Adaptive Regression Network for Single Image Super-Resolution and Beyond](https://mlsanity.com/paper/2105.10422/) (2021)
- [Efficient Movie Scene Detection using State-Space Transformers](https://mlsanity.com/paper/2212.14427/) (2022)
- [U-shaped Vision Mamba for Single Image Dehazing](https://mlsanity.com/paper/2402.04139/) (2024)

## Built on by (most cited first, 1 of 1)

- [TIRMamba: A Thermal-Prior-Modulated State-Space Network for Sub-Million-Parameter Infrared Image Super-Resolution](https://mlsanity.com/paper/2610.05182/) (2026)

## Abstract (arXiv)

State space models (SSMs), particularly Mamba, have shown promise in NLP tasks and are increasingly applied to vision tasks. However, most Mamba-based vision models focus on network architecture and scan paths, with little attention to the SSM module. In order to explore the potential of SSMs, we modified the calculation process of SSM without increasing the number of parameters to improve the performance on lightweight super-resolution tasks. In this paper, we introduce the First-order State Space Model (FSSM) to improve the original Mamba module, enhancing performance by incorporating token correlations. We apply a first-order hold condition in SSMs, derive the new discretized form, and analyzed cumulative error. Extensive experimental results demonstrate that FSSM improves the performance of MambaIR on five benchmark datasets without additionally increasing the number of parameters, and surpasses current lightweight SR methods, achieving state-of-the-art results.