Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised learning has gained prominence. However, its application at high acceleration rates frequently introduces artifacts, compromising image fidelity. To mitigate this shortcoming, we propose a novel way to train PD-DL networks via carefully-designed perturbations. In particular, we enhance the k-space masking idea of conventional self-supervised learning with a novel consistency term that assesses the model's ability to accurately predict the added perturbations in a sparse domain, leading to more reliable and artifact-free reconstructions. The results obtained from the fastMRI knee and brain datasets show that the proposed training strategy effectively reduces aliasing artifacts and mitigates noise amplification at high acceleration rates, outperforming state-of-the-art self-supervised methods both visually and quantitatively.

Physics-driven deep learning (PD-DL) approaches have become popular for improved reconstruction of fast magnetic resonance imaging (MRI) scans. Though PD-DL offers higher acceleration rates than existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. A key challenge is generalization to rare pathologies or different populations, noted in multiple studies, with fine-tuning on target populations suggested for improvement. However, current approaches for PD-DL training require access to raw k-space measurements, which is typically only available at specialized MRI centers that have research agreements for such data access. This is especially an issue for rural and under-resourced areas, where commercial MRI scanners only provide access to a final reconstructed image. To tackle these challenges, we propose Compressibility-inspired Unsupervised Learning via Parallel Imaging Fidelity (CUPID) for high-quality PD-DL training using only routine clinical reconstructed images exported from an MRI scanner. CUPID evaluates output quality with a compressibility-based approach while ensuring that the output stays consistent with the clinical parallel imaging reconstruction through well-designed perturbations. Our results show CUPID achieves similar quality to established PD-DL training that requires k-space data while outperforming compressed sensing (CS) and diffusion-based generative methods. We further demonstrate its effectiveness in a zero-shot training setup for retrospectively and prospectively sub-sampled acquisitions, attesting to its minimal training burden. As an approach that radically deviates from existing strategies, CUPID presents an opportunity to provide broader access to fast MRI for remote and rural populations in an attempt to reduce the obstacles associated with this expensive imaging modality. Code is available at https://github.com/ualcalar17/CUPID.

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our time-embedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly. Code available at https://github.com/JN-Yun/TE-Unrolling-MRI.