Magnetic resonance imaging (MRI) reconstruction under realistic acquisition conditions can be fundamentally viewed as estimating the underlying k-space distribution from incomplete and noise-corrupted measurements. While diffusion models have recently shown strong potential as generative prior for inverse problems,existingapproachesstruggletohandlenoisyreconstruction settings, especially when operating directly in k-space domain. In this work, we propose a unified high-dimensional k-space reconstruction framework tailored for noisy inverse problems, whichenhancesdiffusion-based solversthroughrepresentation lifting.Ratherthanmodifyingthe underlying optimization procedures, the proposed framework augments the data representation space, enabling existing diffusion-based solvers to operate on enriched k-space embeddings with improved expressiveness. Extensive experiments on both in-house and public datasets across varying noise levels and undersampled factors demonstrate that the proposed frame work consistently improves reconstruction quality for multiple diffusion-based inverse solvers. Notably, the largest gains are observed in high-noise regimes, which is consistent with our theoretical analysis of error propagation under high-dimensional representation. These results suggest that high-dimensional representation provides a general and model-agnostic mechanism for improving diffusion-based MRI reconstruction in noisy settings, offering a new perspective on robust k-space generative modeling for practical inverse problems. The code will be available at https://github.com/yqx7150/HEP-MRIRec.
Accelerated magnetic resonance imaging (MRI) enabled by the training of deep learning (DL)-based image recon. models requires large and diverse raw k-space datasets. In most clinical MRI applications, due to storage and patient privacy concerns, raw k-space data is discarded and magnitude-only images are the only component saved. Consequently, a large portion of the DL-based MRI recon. literature has either relied on small training datasets or has used one of the few available open-source k-space datasets. At the same time, the growing number of anonymized magnitude-only image registries/databases motivates the development of techniques that can use them as training datasets for generalizable DL-based recon. models. Here we propose to address this challenge by employing a generative approach based on conditional score-based diffusion models (SBDMs): given a magnitude-only MR image, it synthesizes a phase map (in the image domain) that realistically corresponds to the magnitude-only image. We evaluate its generative capabilities in a downstream DL-based recon. task whereby a large k-space dataset is generated by combining the SBDM-synthesized phase-maps and the corresponding magnitude-only images, and this k-space dataset is then used to train a DL model for accelerated MRI recon. We compare the performance of the resulting DL model versus those trained according to (a) a naive approach that uses smooth phase, (b) a k-space training dataset generated using synthesized phase maps derived from a generative adversarial network, and (c) the ground truth k-space data. Our results suggest that the DL model trained from SBDM-synthesized k-space data outperforms the other approaches in terms of quantitative metrics as well as qualitatively observed recon. fidelity, i.e., whether the reconstructed images include erroneous or hallucinated features that could adversely impact diagnostic accuracy.
M. Berk Sahin, Dilek Yalcinkaya, Abolfazl Hashemi +1
Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time-conditioning mechanisms, and require offline coil sensitivity estimation. This results in limited interpretability of the reconstruction process and reduced flexibility in the acquisition setup. To address these limitations, we jointly reconstruct the image and the coil sensitivities by combining the parameter-efficient product-of-Gaussian-mixture diffusion model as an image prior with a classical smoothness prior on the coil sensitivities. The proposed method is fast and robust to both contrast and anatomical distribution shifts as well as changing k-space trajectories. Finally, we propose a more expressive parameterization of the image prior which improves results in denoising and magnetic resonance image 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.