# Progressive Split Mamba: Effective State Space Modelling for Image Restoration

arXiv: https://arxiv.org/abs/2603.09171 · HTML: https://mlsanity.com/paper/2603.09171/

## Key facts

- Cited by 1 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 34 of its 40 references that are in the map.
- First posted on arXiv 10 Mar 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, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Fast, Accurate, and Lightweight Super-Resolution with Cascading Residual Network](https://mlsanity.com/paper/1803.08664/) (2018)
- [Residual Non-local Attention Networks for Image Restoration](https://mlsanity.com/paper/1903.10082/) (2019)
- [VRT: A Video Restoration Transformer](https://mlsanity.com/paper/2201.12288/) (2022)
- [Efficient Long-Range Attention Network for Image Super-resolution](https://mlsanity.com/paper/2203.06697/) (2022)
- [Compression Artifacts Reduction by a Deep Convolutional Network](https://mlsanity.com/paper/1504.06993/) (2015)
- [Dual Aggregation Transformer for Image Super-Resolution](https://mlsanity.com/paper/2308.03364/) (2023)
- [MambaIRv2: Attentive State Space Restoration](https://mlsanity.com/paper/2411.15269/) (2024)
- [Accurate Image Restoration with Attention Retractable Transformer](https://mlsanity.com/paper/2210.01427/) (2022)
- [HAT: Hybrid Attention Transformer for Image Restoration](https://mlsanity.com/paper/2309.05239/) (2023)
- [FreqMamba: Viewing Mamba from a Frequency Perspective for Image Deraining](https://mlsanity.com/paper/2404.09476/) (2024)
- [MambaLLIE: Implicit Retinex-Aware Low Light Enhancement with Global-then-Local State Space](https://mlsanity.com/paper/2405.16105/) (2024)
- [MaIR: A Locality- and Continuity-Preserving Mamba for Image Restoration](https://mlsanity.com/paper/2412.20066/) (2024)

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

- [TTTIR: Unlocking Instance-Specific State Evolution via Test-Time Training for Image Restoration](https://mlsanity.com/paper/2609.26151/) (2026)

## Abstract (arXiv)

Image restoration requires simultaneously preserving fine-grained local structures and maintaining long-range spatial coherence. While convolutional networks struggle with limited receptive fields, and Transformers incur quadratic complexity for global attention, recent State Space Models (SSMs), such as Mamba, provide an appealing linear-time alternative for long-range dependency modelling. However, naively extending Mamba to 2D images exposes two intrinsic shortcomings. First, flattening 2D feature maps into 1D sequences disrupts spatial topology, leading to locality distortion that hampers precise structural recovery. Second, the stability-driven recurrent dynamics of SSMs induce long-range decay, progressively attenuating information across distant spatial positions and weakening global consistency. Together, these effects limit the effectiveness of state-space modelling in high-fidelity restoration. We propose Progressive Split-Mamba (PS-Mamba), a topology-aware hierarchical state-space framework designed to reconcile locality preservation with efficient global propagation. Instead of sequentially flattening entire feature maps, PS-Mamba performs geometry-consistent partitioning, maintaining neighbourhood integrity prior to state-space processing. A progressive split hierarchy (halves, quadrants, octants) enables structured multi-scale modelling while retaining linear complexity. To counteract long-range decay, we introduce symmetric cross-scale shortcut pathways that directly transmit low-frequency global context across hierarchical levels, stabilising information flow over large spatial extents. Extensive experiments on super-resolution, denoising, and JPEG artifact reduction show consistent improvements over recent Mamba-based and attention-based models with a clear margin.