Hankel Subspace Self-Supervised Learning for Parallel MRI Reconstruction

Self-supervised deep learning-based methods have shown great promise for accelerated magnetic resonance imaging (MRI) reconstruction, achieving high image quality without requiring fully sampled data for training. These methods typically partition the acquired data into two disjoint subsets to construct input-target pairs for optimizing the reconstruction network. However, existing approaches perform this partition exclusively within the spatial frequency (k-space) domain, leaving the coil dimension unexplored. To enforce full exploitation of signal correlation across receiver coils, we propose CoilDrop-MRI, which applies coil-wise dropout to the input and uses the dropped data as training targets in a self-supervised framework. This method is integrated into unrolled architectures in both image-domain (SENSE) and k-space (SPIRiT) formulations. We further demonstrate its versatility by extending CoilDrop-MRI to multi-shot, phase-corrected diffusion MRI (dMRI) reconstruction. CoilDrop-MRI is extensively validated on multi-site, multi-field-strength (0.3T, 0.55T, and 3T), and multi-modality (T1-weighted, T2-weighted, T2-FLAIR, and dMRI) datasets and consistently outperforms state-of-the-art self-supervised methods, achieving quality comparable to supervised reconstruction methods without requiring fully sampled reference training data. Moreover, CoilDrop-MRI exhibits strong data efficiency and robust generalization across imaging conditions, establishing it as a practical and versatile framework for self-supervised parallel MRI reconstruction.

Accelerated magnetic resonance imaging (MRI) aims to recover the k-space signal from acquired measurements, where accurate estimation of missing samples is essential for high-fidelity reconstruction. Existing k-space reconstruction methods estimate missing samples through interpolation operators or structure priors defined on discrete sampling grids. Although these formulations effectively exploit local interpolation relationships and global k-space redundancy, they reconstruct only discrete frequency coefficients and therefore do not explicitly model the underlying continuous signal. To overcome this limitation, we propose K-space Gaussian Representation (KGR), the first explicit continuous representation formulated directly in the native k-space domain. Rather than estimating unknown samples on discrete grids, KGR parameterizes the continuous signal using Gabor-Gaussian primitives with shared spatial geometry, yielding a compact representation that naturally preserves inter-coil correlations. Because unconstrained continuous fitting does not necessarily satisfy the intrinsic structural properties of multi-coil signal, the estimated representation is projected onto a low-rank manifold to enforce the algebraic constraints arising from smoothly varying phase and coil redundancy. A frequency-adaptive fitting strategy accommodates the heterogeneous characteristics of different k-space regions. Comprehensive validation across multiple datasets and sampling schemes shows consistent improvements over representative reconstruction baselines in both quantitative metrics and visual quality. These results suggest that explicit continuous parameterization of native k-space provides a principled framework for integrating continuous signal modeling with structured low-rank reconstruction.

MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to average over feasible reconstructions and suppress high-frequency anatomy. We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction. Leveraging discrete priors proven effective in visual autoregressive modeling, our method restricts the solution to compact sequences of codebook tokens, enabling sharp reconstructions even from extremely sparse measurements. This discrete autoregressive formulation also aligns naturally with modern large language model post-training techniques. Building on this observation, we introduce on-policy privileged information distillation for visual autoregressive modeling, where a teacher is provided training only privileged context that is unavailable at inference, in our case fully sampled acquisitions, and supervises a student trained on its own rollouts, leading to consistent reconstruction gains. Through extensive experiments on the fastMRI benchmark, we show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling. Project website is here.