Diffusion-based arbitrary-scale magnetic resonance image super-resolution via progressive k-space reconstruction and denoising

Acquiring high-resolution Magnetic resonance (MR) images is challenging due to constraints such as hardware limitations and acquisition times. Super-resolution (SR) techniques offer a potential solution to enhance MR image quality without changing the magnetic resonance imaging (MRI) hardware. However, typical SR methods are designed for fixed upsampling scales and often produce over-smoothed images that lack fine textures and edge details. To address these issues, we propose a unified diffusion-based framework for arbitrary-scale in-plane MR image SR, dubbed Progressive Reconstruction and Denoising Diffusion Model (PRDDiff). Specifically, the forward diffusion process of PRDDiff gradually masks out high-frequency components and adds Gaussian noise to simulate the downsampling process in MRI. To reverse this process, we propose an Adaptive Resolution Restoration Network (ARRNet), which introduces a current step corresponding to the resolution of input MR image and an ending step corresponding to the target resolution. This design guide the ARRNet to recovering the clean MR image at the target resolution from input MR image. The SR process starts from an MR image at the initial resolution and gradually enhances them to higher resolution by progressively reconstructing high-frequency components and removing the noise based on the recovered MR image from ARRNet. Furthermore, we design a multi-stage SR strategy that incrementally enhances resolution through multiple sequential stages to further improve recovery accuracy. Each stage utilizes a set number of sampling steps from PRDDiff, guided by a specific ending step, to recover details pertinent to the predefined intermediate resolution. We conduct extensive experiments on fastMRI knee dataset, fastMRI brain dataset, our real-collected LR-HR brain dataset, and clinical pediatric cerebral palsy (CP) dataset, including T1-weighted and T2-weighted images for the brain and proton density-weighted images for the knee. The results demonstrate that PRDDiff outperforms previous MR image super-resolution methods in term of reconstruction accuracy, generalization, and downstream lesion segmentation accuracy and CP classification performance. The code is publicly available at https://github.com/Jiazhen-Wang/PRDDiff-main.