HD-MCVN: hybrid-domain multi-contrast variational network for MRI super-resolution

<i>Objective.</i>Magnetic resonance imaging (MRI) is essential in medical diagnostics, but its resolution is often limited by factors such as scan time, signal-to-noise ratio, and hardware constraints. With the development of deep learning, multi-contrast super-resolution methods have gradually become a research hotspot. However, most existing approaches rely solely on image-domain information, overlooking valuable<i>k</i>-space data. Moreover, their fusion strategies across different modalities are often loosely defined and lack physical interpretability.<i>Approach.</i>We propose a hybrid-domain multi-contrast variational network (HD-MCVN), which integrates variational optimization with deep learning, explicitly modeling cross-modal relationships. Specifically, by integrating frequency-domain<i>k</i>-space information, structural priors from high-resolution reference images, and similar texture details across modalities, HD-MCVN establishes a synergistic global-structural-texture framework that enables high-quality MR reconstruction from multiple perspectives. The reconstruction process is jointly optimized in both the image and<i>k</i>-space domains. In the<i>k</i>-space domain, a data fidelity layer is proposed to enforce global consistency and ensure the reliability of the reconstructed data. In the image domain, the proposed structural texture refinement layer improves the anatomical accuracy by recovering high-frequency components and enhancing fine texture details. Additionally, we design a hybrid texture loss function to supervise the reconstruction of both image content and edge details.<i>Main results.</i>Experimental results demonstrate that HD-MCVN achieves superior performance across multiple MRI datasets. Under a representative ×4 undersampling setting, HD-MCVN achieves PSNR improvements of approximately 0.3-0.6 dB and SSIM gains of 0.001-0.003, together with a reduction in HFEN, indicating improved structural fidelity and enhanced preservation of fine anatomical details.<i>Significance.</i>The proposed HD-MCVN provides a novel, interpretable framework for MRI super-resolution by effectively fusing hybrid-domain information and multi-contrast priors. Its superior performance and inherent interpretability significantly enhance its clinical reliability, underscoring its substantial potential for improving medical image analysis and diagnostic practice.