Training Physics-Driven Deep Learning Reconstruction without Raw Data Access for Equitable Fast MRI

Physics-driven deep learning (PD-DL) approaches have become popular for improved reconstruction of fast magnetic resonance imaging (MRI) scans. Even though PD-DL offers higher acceleration rates compared to existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. One impediment for their deployment is the difficulties with generalization to pathologies or population groups that are not well-represented in training sets. This has been noted in several studies, and fine-tuning on target populations to improve reconstruction has been suggested. 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 underserved 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 the goodness of the output 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 that CUPID achieves similar quality compared to well-established PD-DL training strategies that require raw k-space data access, while outperforming conventional compressed sensing (CS) and state-of-the-art generative methods. We also demonstrate its effectiveness in a zero-shot training setup for retrospectively and prospectively sub-sampled acquisitions, attesting to its minimal training burden.

Zero-Shot Adaptation for Approximate Posterior Sampling of Diffusion Models in Inverse Problems

Diffusion models have emerged as powerful generative techniques for solving inverse problems. Despite their success in a variety of inverse problems in imaging, these models require many steps to converge, leading to slow inference time. Recently, there has been a trend in diffusion models for employing sophisticated noise schedules that involve more frequent iterations of timesteps at lower noise levels, thereby improving image generation and convergence speed. However, application of these ideas for solving inverse problems with diffusion models remain challenging, as these noise schedules do not perform well when using empirical tuning for the forward model log-likelihood term weights. To tackle these challenges, we propose zero-shot approximate posterior sampling (ZAPS) that leverages connections to zero-shot physics-driven deep learning. ZAPS fixes the number of sampling steps, and uses zero-shot training with a physics-guided loss function to learn log-likelihood weights at each irregular timestep. We apply ZAPS to the recently proposed diffusion posterior sampling method as baseline, though ZAPS can also be used with other posterior sampling diffusion models. We further approximate the Hessian of the logarithm of the prior using a diagonalization approach with learnable diagonal entries for computational efficiency. These parameters are optimized over a fixed number of epochs with a given computational budget. Our results for various noisy inverse problems, including Gaussian and motion deblurring, inpainting, and super-resolution show that ZAPS reduces inference time, provides robustness to irregular noise schedules and improves reconstruction quality. Code is available at https://github.com/ualcalar17/ZAPS