Self-Consistent Nested Diffusion Bridge for Accelerated MRI Reconstruction

TL;DR

The paper tackles magnitude-image-based MRI reconstruction by formulating accelerated MRI as a bi-directional translation between under-sampled and fully-sampled magnitude images. It introduces the Self-Consistent Nested Diffusion Bridge (SC-NDB), a dual nested diffusion-bridge framework with a self-consistency constraint, and a Contour Decomposition Embedding Module (CDEM) that leverages contourlet-based multi-scale, directional structure. The approach uses a Brownian-bridge diffusion formulation and self-consistency losses to better capture priors from the source magnitude images, enabling more faithful intermediate-state predictions. Extensive experiments on fastMRI and IXI show SC-NDB achieving state-of-the-art results among magnitude-based and non-magnitude-based diffusion models, with improved detail preservation and practical inference efficiency. The work demonstrates the potential of magnitude-image diffusion priors for clinically realistic MRI reconstruction and points to future work on efficiency and cross-domain generalization.

Abstract

Accelerated MRI reconstruction plays a vital role in reducing scan time while preserving image quality. While most existing methods rely on complex-valued image-space or k-space data, these formats are often inaccessible in clinical practice due to proprietary reconstruction pipelines, leaving only magnitude images stored in DICOM files. To address this gap, we focus on the underexplored task of magnitude-image-based MRI reconstruction. Recent advancements in diffusion models, particularly denoising diffusion probabilistic models (DDPMs), have demonstrated strong capabilities in modeling image priors. However, their task-agnostic denoising nature limits performance in source-to-target image translation tasks, such as MRI reconstruction. In this work, we propose a novel Self-Consistent Nested Diffusion Bridge (SC-NDB) framework that models accelerated MRI reconstruction as a bi-directional image translation process between under-sampled and fully-sampled magnitude MRI images. SC-NDB introduces a nested diffusion architecture with a self-consistency constraint and reverse bridge diffusion pathways to improve intermediate prediction fidelity and better capture the explicit priors of source images. Furthermore, we incorporate a Contour Decomposition Embedding Module (CDEM) to inject structural and textural knowledge by leveraging Laplacian pyramids and directional filter banks. Extensive experiments on the fastMRI and IXI datasets demonstrate that our method achieves state-of-the-art performance compared to both magnitude-based and non-magnitude-based diffusion models, confirming the effectiveness and clinical relevance of SC-NDB.

Figures (11)

• Figure 1: The framework of the SC-NDB involves two nested diffusion bridges between deterministically under-sampled and fully-sampled MR magnitude images.
• Figure 2: Comparisons with state-of-the-art methods in terms of PSNR and SSIM results on the fastMRI knee dataset.
• Figure 3: Categorized reconstruction methods based on data types: image-space, k-space, and magnitude-image. Our proposed method specifically focuses on the magnitude image scenario.
• Figure 4: Visual comparison of sparsity representations using (a) traditional Wavelet Transform and (b) Contourlet Transform.
• Figure 5: Denosing network with time and contourlet decomposition embedding.