The proposed K-space Gaussian Representation (KGR), the first explicit continuous representation formulated directly in the native k-space domain, suggests that explicit continuous parameterization of native k-space provides a principled framework for integrating continuous signal modeling with structured low-rank reconstruction.
Abstract
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.
A model-driven bilevel optimization framework that couples SENSE-based image reconstruction with SPIRiT-based k-space calibration through shared CSMs, and introduces a deep-prior-guided regularization strategy that preserves the structure of classical linear regularizers while adaptively learning spatially varying regularization weights from denoised intermediate reconstructions.
Weipeng Chen, Yan-Ran Li, Raymond H. Chan et al.· Journal of Mathematical Imag...· 0 citations
In this work, we consider a structured tensor approximation problem, where only a limited number of lateral slices are observed. The proposed algorithm , called Basis and Manifold prior Tensor Approximation (BMTA), exploits both global and local structures of the evolution of a global tensor. Specifically, BMTA integrates two signal models: (i) a quasi-basis model that captures smooth global variations along a physical trajectory, and (ii) a manifold-guided interpolation model that characterizes local relationships among tensor slices. A low-rank Tucker reconstruction framework is incorporated to efficiently capture the priors, resulting in coefficients for basis function estimation and a tensor optimization. In addition, we provide a theoretical analysis which establishes a non-asymptotic reconstruction error bound that characterizes the effects of sampling complexity, optimization convergence, and model mismatch. Numerical experiments are performed on both synthetic and real-world datasets, including quantum chemistry and spatiotemporal sensing applications.
Jeongmin Chae, Usama Saleem, Selin Bac et al.· 0 citations
This work investigates the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction, and demonstrates strong consistency of k-space magnitudes across time-frames.
Mahdi Saberi, Y. Alçalar, Merve Gülle et al.· 0 citations
HiGDiff is proposed, a feed-forward hierarchical Gaussian diffusion framework that decomposes reconstruction both spatially and from structure to detail in three distinct CT benchmark datasets.
While multishot interleaved echo‐planar imaging (iEPI) enables higher resolution diffusion kurtosis imaging (DKI) compared to single‐shot EPI, its clinical application is hindered by the lengthy acquisition time. This study proposes a novel model‐based reconstruction approach to accelerate iEPI DKI acquisition.
Jian Lyu, Li Guo, Wen Zhong et al.· Magnetic Resonance in Medici...· 0 citations
Multi-Pool Chemical Exchange Saturation Transfer (CEST) MRI provides valuable metabolic information but is clinically limited by long acquisition times. Although sparse sampling reduces scanning time, reconstructing high-resolution Z-spectra from limited data remains an ill-posed inverse problem. Conventional interpolation and generic Implicit Neural Rep-resentations (INRs) often lack physical constraints, leading to spectral artifacts and physically invalid signals. To address this, we propose Lorentz Encoding (LE), a physics-informed framework that formulates CEST reconstruction as a self-supervised reconstruction task via implicit continuous coordinate learning. Unlike generic positional encodings, LE regularizes the continuous spectral mapping by projecting sparse coordinates into a physically constrained space governed by a combination of parametric Lorentzian profiles with learnable basis functions. This mechanism effectively reduces noise and enforces consistency with physical models. Experiments on in vivo human brain data demonstrate that LE significantly outperforms state-of-the-art methods. Specifically, under a 39-point sampling strategy, LE achieves a PSNR of 57.58 dB and an SSIM of 0.9994. Furthermore, the learned physics-informed encodings form a continuous, geometrically ordered trajectory in the latent space, ensuring accurate quantitative metabo-lite mapping (APT, NOE, MT).
Dexuan Li, Yupeng Wu, Chenglong Wang et al.· 0 citations