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 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. Further, 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 use Noisier2Noise to propose a modification of SSDU that we find substantially improves its reconstruction quality and robustness, offering a test set mean-squared-error within 1% of fully supervised training on the fastMRI brain dataset.

本文介绍了如何使用Noisier2Noise框架进行自监督学习，在MRI数据的稀缺情况下，通过数据下采样的方式提高重建质量和鲁棒性，同时解释了SSDU方法的表现原理。

使用可变密度Noisier2Noise的子抽样进行自监督MR图像重建的理论框架