Frequency Error-Guided Under-sampling Optimization for Multi-Contrast MRI Reconstruction

TL;DR

The paper tackles the challenge of accelerating multi-contrast MRI by jointly learning under-sampling patterns and reconstructions with physical interpretability. It introduces JUF-MRI, a two-stage framework where a conditional diffusion model yields a frequency error prior (FEP) that guides a differentiable, model-driven unfolding network to optimize both the sampling mask and reconstruction. A spatial-alignment module and a reference-feature decomposition strategy improve cross-contrast information transfer, and a novel frequency-domain loss emphasizes high-frequency detail. Across IXI, BraTS2018, and FastMRI, JUF-MRI achieves state-of-the-art performance at accelerations from 4× to 30× while maintaining a compact model and efficient inference, highlighting the practical potential for clinical deployment.

Abstract

Magnetic resonance imaging (MRI) plays a vital role in clinical diagnostics, yet it remains hindered by long acquisition times and motion artifacts. Multi-contrast MRI reconstruction has emerged as a promising direction by leveraging complementary information from fully-sampled reference scans. However, existing approaches suffer from three major limitations: (1) superficial reference fusion strategies, such as simple concatenation, (2) insufficient utilization of the complementary information provided by the reference contrast, and (3) fixed under-sampling patterns. We propose an efficient and interpretable frequency error-guided reconstruction framework to tackle these issues. We first employ a conditional diffusion model to learn a Frequency Error Prior (FEP), which is then incorporated into a unified framework for jointly optimizing both the under-sampling pattern and the reconstruction network. The proposed reconstruction model employs a model-driven deep unfolding framework that jointly exploits frequency- and image-domain information. In addition, a spatial alignment module and a reference feature decomposition strategy are incorporated to improve reconstruction quality and bridge model-based optimization with data-driven learning for improved physical interpretability. Comprehensive validation across multiple imaging modalities, acceleration rates (4-30x), and sampling schemes demonstrates consistent superiority over state-of-the-art methods in both quantitative metrics and visual quality. All codes are available at https://github.com/fangxinming/JUF-MRI.

Figures (15)

• Figure 1: An illustration of the proposed JUF-MRI framework, which consists of two stages. In Stage 1, a frequency error prior $r$ is obtained using a conditional diffusion model. In Stage 2, the under-sampling pattern and the reconstruction network parameters are jointly optimized.
• Figure 2: The forward and backward processes of the proposed Conditional Diffusion Model (CDM). In the backward process, the conditional image $X_{\text{condi}}$ and the current noisy image $X_t$ are concatenated along the channel dimension. This concatenated input, along with the current timestep $t$, is then fed into the diffusion U-Net model to guide the prediction of the noise.
• Figure 3: The testing procedure for the trained reconstruction network. The process highlighted by the red box represents the practical multi-contrast MRI reconstruction pipeline.
• Figure 4: The architecture of the proposed deep unfolding reconstruction network, which consists of three components: the initialization module, the iterative sub-modules, and the reconstruction layer (RecLayer).
• Figure 5: The details of the iterative sub-module in the reconstruction network. This module is responsible for the iterative optimization of four parameters: $X$, $S$, $K$, and $D$. Specifically, $K_{x}^{t-1}$ denotes the $k$-space data derived from the intermediate image $X^{t-1}$ via Fourier transform during the reconstruction process, $X_{\text{dc}}$ refers to the output of the data consistency layer applied to $X^{t-1}$, and $J_{n \times n}$ denotes an $n \times n$ matrix with every entry equal to $1$.