The existence of completely aligned and paired multi-modal neuroimaging data has proved its effectiveness in diagnosis of brain diseases. However, collecting the full set of well-aligned and paired data is expensive or even impractical, since the practical difficulties may include high cost, long time acquisition, image corruption, and privacy issues. A realistic solution is to explore either an unsupervised learning or a semi-supervised learning to synthesize the absent neuroimaging data. In this paper, we are the first one to comprehensively approach cross-modality neuroimage synthesis task from different perspectives, which include the level of the supervision (especially for weakly-supervised and unsupervised), loss function, evaluation metrics, the range of modality synthesis, datasets (aligned, private and public) and the synthesis-based downstream tasks. To begin with, we highlight several opening challenges for cross-modality neuroimage sysnthesis. Then we summarize the architecture of cross-modality synthesis under various of supervision level. In addition, we provide in-depth analysis of how cross-modality neuroimage synthesis can improve the performance of different downstream tasks. Finally, we re-evaluate the open challenges and point out the future directions for the remaining challenges. All resources are available at https://github.com/M-3LAB/awesome-multimodal-brain-image-systhesis
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