In recent years, there has been attention on leveraging the statistical modeling capabilities of neural networks for reconstructing sub-sampled Magnetic Resonance Imaging (MRI) data. Most proposed methods assume the existence of a representative fully-sampled dataset and use fully-supervised training. However, for many applications, fully sampled training data is not available, and may be highly impractical to acquire. The development and understanding of self-supervised methods, which use only sub-sampled data for training, are therefore highly desirable. This work extends the Noisier2Noise framework, which was originally constructed for self-supervised denoising tasks, to variable density sub-sampled MRI data. We use the Noisier2Noise framework to analytically explain the performance of Self-Supervised Learning via Data Undersampling (SSDU), a recently proposed method that performs well in practice but until now lacked theoretical justification. We also show that SSDU's reconstruction quality and robustness improves when the partitioned subsets have the same type of distribution as the original sampling mask.

翻译：近年来,人们一直关注利用神经网络的统计模型能力来重建次级抽样磁共振成像(MRI)数据的重建。大多数拟议方法假定存在一个有代表性的全抽样数据集,并使用完全监督的培训。然而,在许多应用中,没有完全抽样的培训数据,而且可能非常不切实际。因此,开发和理解仅使用次级抽样数据进行培训的自我监督方法是非常可取的。这项工作将最初为自我监督的分解任务而建立的Noisier2Noise框架延伸至可变密度分抽样的MRI数据。我们使用Noiser2Noise框架来分析通过数据抽查(SSDU)进行自我抽样学习的绩效,这是最近提出的方法,在实践上表现良好,但至今还缺乏理论依据。我们还表明,当分片子的分布类型与原始取样面具相同时,SSDU的重建质量和稳健性会提高。