Cross-modality synthesis (CMS), super-resolution (SR), and their combination (CMSR) have been extensively studied for magnetic resonance imaging (MRI). Their primary goals are to enhance the imaging quality by synthesizing the desired modality and reducing the slice thickness. Despite the promising synthetic results, these techniques are often tailored to specific tasks, thereby limiting their adaptability to complex clinical scenarios. Therefore, it is crucial to build a unified network that can handle various image synthesis tasks with arbitrary requirements of modality and resolution settings, so that the resources for training and deploying the models can be greatly reduced. However, none of the previous works is capable of performing CMS, SR, and CMSR using a unified network. Moreover, these MRI reconstruction methods often treat alias frequencies improperly, resulting in suboptimal detail restoration. In this paper, we propose a Unified Co-Modulated Alias-free framework (Uni-COAL) to accomplish the aforementioned tasks with a single network. The co-modulation design of the image-conditioned and stochastic attribute representations ensures the consistency between CMS and SR, while simultaneously accommodating arbitrary combinations of input/output modalities and thickness. The generator of Uni-COAL is also designed to be alias-free based on the Shannon-Nyquist signal processing framework, ensuring effective suppression of alias frequencies. Additionally, we leverage the semantic prior of Segment Anything Model (SAM) to guide Uni-COAL, ensuring a more authentic preservation of anatomical structures during synthesis. Experiments on three datasets demonstrate that Uni-COAL outperforms the alternatives in CMS, SR, and CMSR tasks for MR images, which highlights its generalizability to wide-range applications.
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