Hybrid learning: a combination of self-supervised and supervised learning for joint MRI reconstruction and denoising in low-field MRI

Objective. Deep learning has demonstrated strong potential for magnetic resonance imaging (MRI) reconstruction. However, conventional supervised learning requires high-quality, high-signal-to-noise-ratio (SNR) reference data for network training, which are often difficult or impossible to obtain, particularly in low-field MRI. Self-supervised learning (SSL) eliminates the need for reference training data but may suffer from degraded performance under low-SNR conditions. To address these limitations, we propose hybrid learning, a new training framework that integrates self-supervised and supervised learning for joint MRI reconstruction and denoising when only low-SNR training data are available. Approach. Hybrid learning is implemented in two sequential stages. In the first stage, SSL is applied to fully sampled low-SNR data to generate higher-quality pseudo-references. In the second stage, these pseudo-references are then used as targets for supervised learning to reconstruct and denoise undersampled, noisy data. The proposed method was evaluated in four experiments using simulated and real noisy MRI data of the breast, lung, and brain across different field strengths (0.3 T to 3 T), sampling trajectories (Cartesian, spiral, and radial), noise levels, and undersampling ratios. Main Results. Hybrid learning consistently improved reconstruction quality relative to both supervised and self-supervised baselines under different acceleration rates, noise levels, and sampling patterns in all experiments. Compared with standard supervised learning using noisy references, it achieved up to 167.70% higher structural similarity index measure (SSIM), 95.41% lower normalized mean squared error (NMSE), and 90.70% lower high-frequency error norm (HFEN). Compared with standard SSL, it achieved up to 23.88% higher SSIM, 60.85% lower NMSE, and 49.13% lower HFEN. Significance. Hybrid learning enables improved MRI reconstruction under low-SNR imaging conditions by jointly addressing noise and undersampling. It provides a practical solution for robust deep learning-based reconstruction and is particularly well suited for applications such as low-field MRI, where image quality is limited by reduced SNR.