MIGA:Shared-Geometry Gaussian Representation with Implicit Amplitude Modeling for Accelerated 3D Multi-Echo MRI

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 \href{https://yilmazkorkmaz1.github.io/discrete-mri-reconstruction-opd/}{here}.

To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear extension of the linear subspace model, then used it to represent and reconstruct MRE image repetitions from undersampled k-space data. The network weights were learned using a multi-level k-space consistent loss. To further enhance reconstruction quality, phase-contrast specific magnitude and phase priors were incorporated, including the similarity of anatomical structures and smoothness of wave-induced harmonic displacement. Experiments were conducted using both 3D gradient-echo spiral and multi-slice spin-echo spiral MRE datasets. Compared to the conventional linear subspace-based approaches, the nonlinear network representation method was able to produce superior image reconstruction with suppressed noise and artifacts from a single in-plane spiral arm per MRE repetition (e.g., 2mm isotropic resolution in 1 min with a total R=10), yielding comparable stiffness estimation to the fully sampled data. This work demonstrated the feasibility of using deep network representations to model and reconstruct MRE images from highly-undersampled data, a nonlinear extension of the subspace-based approaches.