# FaRMamba: Frequency-based learning and Reconstruction aided Mamba for Medical Segmentation

arXiv: https://arxiv.org/abs/2507.20056 · HTML: https://mlsanity.com/paper/2507.20056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mamba for medical image analysis, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 25 of its 39 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [Deep Learning for Segmentation using an Open Large-Scale Dataset in 2D Echocardiography](https://mlsanity.com/paper/1908.06948/) (2019)
- [U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation](https://mlsanity.com/paper/2406.02918/) (2024)
- [UNetFormer: A UNet-like Transformer for Efficient Semantic Segmentation of Remote Sensing Urban Scene Imagery](https://mlsanity.com/paper/2109.08937/) (2021)
- [Self Pre-training with Masked Autoencoders for Medical Image Classification and Segmentation](https://mlsanity.com/paper/2203.05573/) (2022)
- [Y-Net: Joint Segmentation and Classification for Diagnosis of Breast Biopsy Images](https://mlsanity.com/paper/1806.01313/) (2018)
- [State-space Models with Layer-wise Nonlinearity are Universal Approximators with Exponential Decaying Memory](https://mlsanity.com/paper/2309.13414/) (2023)
- [P-Mamba: Marrying Perona Malik Diffusion with Mamba for Efficient Pediatric Echocardiographic Left Ventricular Segmentation](https://mlsanity.com/paper/2402.08506/) (2024)
- [MambaMIR: An Arbitrary-Masked Mamba for Joint Medical Image Reconstruction and Uncertainty Estimation](https://mlsanity.com/paper/2402.18451/) (2024)
- [Tuning Frequency Bias of State Space Models](https://mlsanity.com/paper/2410.02035/) (2024)
- [EM-Net: Efficient Channel and Frequency Learning with Mamba for 3D Medical Image Segmentation](https://mlsanity.com/paper/2409.17675/) (2024)
- [Self-Supervised Alignment Learning for Medical Image Segmentation](https://mlsanity.com/paper/2406.15699/) (2024)
- [Domain Influence in MRI Medical Image Segmentation: spatial versus k-space inputs](https://mlsanity.com/paper/2407.01367/) (2024)
- [GlobalMamba: Global Image Serialization for Vision Mamba](https://mlsanity.com/paper/2410.10316/) (2024)

## Abstract (arXiv)

Accurate medical image segmentation remains challenging due to blurred lesion boundaries (LBA), loss of high-frequency details (LHD), and difficulty in modeling long-range anatomical structures (DC-LRSS). Vision Mamba employs one-dimensional causal state-space recurrence to efficiently model global dependencies, thereby substantially mitigating DC-LRSS. However, its patch tokenization and 1D serialization disrupt local pixel adjacency and impose a low-pass filtering effect, resulting in Local High-frequency Information Capture Deficiency (LHICD) and two-dimensional Spatial Structure Degradation (2D-SSD), which in turn exacerbate LBA and LHD. In this work, we propose FaRMamba, a novel extension that explicitly addresses LHICD and 2D-SSD through two complementary modules. A Multi-Scale Frequency Transform Module (MSFM) restores attenuated high-frequency cues by isolating and reconstructing multi-band spectra via wavelet, cosine, and Fourier transforms. A Self-Supervised Reconstruction Auxiliary Encoder (SSRAE) enforces pixel-level reconstruction on the shared Mamba encoder to recover full 2D spatial correlations, enhancing both fine textures and global context. Extensive evaluations on CAMUS echocardiography, MRI-based Mouse-cochlea, and Kvasir-Seg endoscopy demonstrate that FaRMamba consistently outperforms competitive CNN-Transformer hybrids and existing Mamba variants, delivering superior boundary accuracy, detail preservation, and global coherence without prohibitive computational overhead. This work provides a flexible frequency-aware framework for future segmentation models that directly mitigates core challenges in medical imaging.