Magnetic Resonance Imaging (MRI) represents an important diagnostic modality; however, its inherently slow acquisition process poses challenges in obtaining fully-sampled $k$-space data under motion. In the absence of fully-sampled acquisitions, serving as ground truths, training deep learning algorithms in a supervised manner to predict the underlying ground truth image becomes challenging. To address this limitation, self-supervised methods have emerged as a viable alternative, leveraging available subsampled $k$-space data to train deep neural networks for MRI reconstruction. Nevertheless, these approaches often fall short when compared to supervised methods. We propose Joint Supervised and Self-supervised Learning (JSSL), a novel training approach for deep learning-based MRI reconstruction algorithms aimed at enhancing reconstruction quality in cases where target datasets containing fully-sampled $k$-space measurements are unavailable. JSSL operates by simultaneously training a model in a self-supervised learning setting, using subsampled data from the target dataset(s), and in a supervised learning manner, utilizing datasets with fully-sampled $k$-space data, referred to as proxy datasets. We demonstrate JSSL's efficacy using subsampled prostate or cardiac MRI data as the target datasets, with fully-sampled brain and knee, or brain, knee and prostate $k$-space acquisitions, respectively, as proxy datasets. Our results showcase substantial improvements over conventional self-supervised methods, validated using common image quality metrics. Furthermore, we provide theoretical motivations for JSSL and establish "rule-of-thumb" guidelines for training MRI reconstruction models. JSSL effectively enhances MRI reconstruction quality in scenarios where fully-sampled $k$-space data is not available, leveraging the strengths of supervised learning by incorporating proxy datasets.

翻译：磁共振成像（MRI）是一种重要的诊断手段；然而，其固有的缓慢采集过程使得在运动条件下获取完全采样的$k$空间数据面临挑战。在缺乏作为真实基准的完全采样采集数据的情况下，以监督方式训练深度学习算法来预测潜在的真实基准图像变得困难。为应对这一局限，自监督方法已成为一种可行的替代方案，利用可用的欠采样$k$空间数据训练深度神经网络进行MRI重建。然而，这些方法通常仍逊色于监督方法。我们提出联合监督与自监督学习（JSSL），这是一种用于基于深度学习的MRI重建算法的新型训练方法，旨在提升在目标数据集缺乏完全采样$k$空间测量时的重建质量。JSSL通过同时以自监督学习方式（使用目标数据集的欠采样数据）和以监督学习方式（利用具有完全采样$k$空间数据的代理数据集）训练模型来运作。我们使用欠采样的前列腺或心脏MRI数据作为目标数据集，并分别以完全采样的大脑和膝盖，或大脑、膝盖及前列腺的$k$空间采集数据作为代理数据集，证明了JSSL的有效性。我们的结果显示，相较于传统的自监督方法，JSSL在常用图像质量指标上取得了显著提升。此外，我们为JSSL提供了理论依据，并建立了训练MRI重建模型的"经验法则"指南。JSSL通过结合代理数据集、利用监督学习的优势，在无法获得完全采样$k$空间数据的情况下，有效提升了MRI重建质量。