Motion artifacts present in magnetic resonance imaging (MRI) can seriously interfere with clinical diagnosis. Removing motion artifacts is a straightforward solution and has been extensively studied. However, paired data are still heavily relied on in recent works and the perturbations in k-space (frequency domain) are not well considered, which limits their applications in the clinical field. To address these issues, we propose a novel unsupervised purification method which leverages pixel-frequency information of noisy MRI images to guide a pre-trained diffusion model to recover clean MRI images. Specifically, considering that motion artifacts are mainly concentrated in high-frequency components in k-space, we utilize the low-frequency components as the guide to ensure correct tissue textures. Additionally, given that high-frequency and pixel information are helpful for recovering shape and detail textures, we design alternate complementary masks to simultaneously destroy the artifact structure and exploit useful information. Quantitative experiments are performed on datasets from different tissues and show that our method achieves superior performance on several metrics. Qualitative evaluations with radiologists also show that our method provides better clinical feedback. Our code is available at https://github.com/medcx/PFAD.
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