PAS-Mamba: Phase-Amplitude-Spatial State Space Model for MRI Reconstruction

TL;DR

PAS-Mamba addresses MRI reconstruction under undersampling by decoupling phase and amplitude in the frequency domain and fusing these with an image-domain path. It introduces Circular Frequency Domain Scanning to respect the concentric geometry of k-space and a Dual-Domain Complementary Fusion Module to enable cross-domain interaction between amplitude, phase, and spatial features, all within a Mamba-based state-space framework. The architecture combines a LocalMamba-enabled image path with separate amplitude and phase branches in the frequency domain, achieving global dependency modeling with linear complexity and improved local detail preservation. Across IXI and fastMRI knee datasets, PAS-Mamba consistently surpasses state-of-the-art methods in PSNR and SSIM across radial and Cartesian undersampling schemes, demonstrating robustness and practical impact for accelerated MRI reconstruction.

Abstract

Joint feature modeling in both the spatial and frequency domains has become a mainstream approach in MRI reconstruction. However, existing methods generally treat the frequency domain as a whole, neglecting the differences in the information carried by its internal components. According to Fourier transform theory, phase and amplitude represent different types of information in the image. Our spectrum swapping experiments show that magnitude mainly reflects pixel-level intensity, while phase predominantly governs image structure. To prevent interference between phase and magnitude feature learning caused by unified frequency-domain modeling, we propose the Phase-Amplitude-Spatial State Space Model (PAS-Mamba) for MRI Reconstruction, a framework that decouples phase and magnitude modeling in the frequency domain and combines it with image-domain features for better reconstruction. In the image domain, LocalMamba preserves spatial locality to sharpen fine anatomical details. In frequency domain, we disentangle amplitude and phase into two specialized branches to avoid representational coupling. To respect the concentric geometry of frequency information, we propose Circular Frequency Domain Scanning (CFDS) to serialize features from low to high frequencies. Finally, a Dual-Domain Complementary Fusion Module (DDCFM) adaptively fuses amplitude phase representations and enables bidirectional exchange between frequency and image domains, delivering superior reconstruction. Extensive experiments on the IXI and fastMRI knee datasets show that PAS-Mamba consistently outperforms state of the art reconstruction methods.

Figures (8)

• Figure 1: Observation of the phase spectrum exchange.
• Figure 2: Motivation: (a) Challenges in MRI reconstruction: the Coupling and Interference of Phase and Amplitude Information, along with the Disruption of the Circularity in the Frequency Domain and Significant Domain Discrepancies, Hinder Direct fusion. (b) To address these issues, we propose a decoupled modeling approach in the frequency domain, which separates the phase and amplitude components. Additionally, a circular scanning method is employed in the frequency domain to align with the concentric circular characteristics of the frequency domain. Furthermore, the Dual-Domain Complementary Fusion Module(DDCFM) is introduced to integrate the phase and amplitude information.
• Figure 3: The overall architecture of PAS-Mamba. Given an undersampled image($I_{in}$), the network splits the input into a spatial-domain branch and a frequency-domain branch. The frequency-domain branch is further divided into amplitude and phase sub-branches. The proposed DDCFM module first integrates the amplitude and phase features to form a complete frequency-domain representation, and then fuses this representation with the spatial-domain features. The fused features are finally fed into the reconstruction head to produce the final reconstructed image($I_{out}$).
• Figure 4: (a) The standard Mamba scanning disrupts local spatial features in the image. (b) LocalMamba Scanning preserves local spatial features in the image.
• Figure 5: (a) In the K-space spectrum, the frequency distribution exhibits a concentric circular structure. Low-frequency components are located at the center, while high-frequency components lie in the peripheral regions. (b) The standard Mamba scanning disrupts the concentric circular structure of the frequency domain. (c) Circular Frequency Domain Scanning (CFDS). This scanning method can generate ordered sequences from low to high frequencies.