ABSTRACT Purpose To develop and evaluate a memory‐efficient and accelerated reconstruction framework for respiratory‐resolved 4D lung MRI using coil sketching and Toeplitz approximation, enabling high‐quality motion‐compensated low‐rank (MoCo‐LR) reconstructions on clinically accessible GPU hardware. Theory and Methods Respiratory‐resolved 4D MRI enables non‐invasive assessment of pulmonary structure and function but is limited by computational and memory demands from large matrices and long acquisitions. We extend the coil sketching framework—previously proposed for 3D imaging—to 4D (3D + time), allowing the data consistency term of compressed‐sensing objective functions to be solved with reduced GPU memory consumption and reconstruction duration while preserving image accuracy. Additionally, we implement Toeplitz approximation to accelerate repeated applications of the normal encoding operator, further reducing computational demand. Finally, we outline a MoCo‐LR regularization technique that uses only forward deformations, improving reconstruction stability over many iterations. Reconstructions were performed across several regularization schemes using a 3D stack‐of‐spirals acquisition and evaluated for memory footprint, speed, and image accuracy. Results The proposed 4D coil sketching method reduced memory usage by ˜3‐fold compared to fully sampled reconstructions and enabled high‐resolution MoCo‐LR reconstructions in < 10 min on < 48 GB GPUs. Toeplitz approximation further reduced runtime with minimal impact on image quality. Compared to conventional coil compression, coil sketching preserved parenchymal signal and structural fidelity in low‐SNR regions. Conclusion Coil sketching and Toeplitz approximation provide a generalizable, hardware‐efficient solution for 4D lung MRI reconstruction. These methods reduce computational barriers, improve reconstruction speed, and maintain image quality, offering a path toward broader clinical adoption of respiratory‐resolved lung MRI.
Plummer et al. (Fri,) studied this question.