VQ-SToRM: Vector-Quantized Smoothness Regularization on Manifolds for Free-Breathing, Ungated Real-Time Cardiac MRI Reconstruction.

Real-time, free-breathing, ungated cardiac magnetic resonance imaging (CMR) is a clinically valuable alternative to conventional breath-held, ECG-gated cine imaging for patients who cannot sustain breath holds or produce reliable cardiac rhythms, including pediatric, arrhythmic, and respiratory-compromised populations. Achieving diagnostic image quality in this setting requires aggressive k-space undersampling and sophisticated reconstruction. Because no fully sampled reference exists for such acquisitions, supervised deep learning is not directly applicable, motivating unsupervised, subject-specific methods. Existing approaches typically rely on low-dimensional continuous latent spaces, which can limit their capacity to represent concurrent cardiac and respiratory motions as distinct states and may suffer from posterior collapse. We introduce VQ-SToRM (Vector-Quantized Smoothness Regularization on Manifolds), an unsupervised framework that adapts the Vector-Quantized Variational Autoencoder to real-time CMR by replacing the continuous latent manifold of prior existing methods with a learned discrete codebook. The encoder, decoder, and codebook are trained jointly on the undersampled non-Cartesian k-t space data of a single subject. On free-breathing, ungated spiral acquisitions from healthy volunteers, VQ-SToRM accurately resolved cardiac and respiratory motion across all phases of the cardiac cycle. A systematic ablation study identified a compact configuration-a codebook of only five embeddings of dimension ten-as optimal, indicating that a small discrete codebook is sufficient to represent the dominant cardiac and respiratory motion content. Compared with V-SToRM and Time-DIP, VQ-SToRM achieved smoother frame-to-frame transitions and comparable or superior signal-to-noise and contrast-to-noise ratios with lower variance across frames and datasets, offering a promising path toward clinically practical real-time CMR.