Gabor Primitives for Accelerated Cardiac Cine MRI Reconstruction
Authors: Wenqi Huang, Veronika Spieker, Nil Stolt-Ansó, Natascha Niessen, Maik Dannecker, Sevgi Gokce Kafali, Sila Kurugol, Julia A. Schnabel, +1 more
Organizations: Chair for AI in Healthcare and Medicine, Technical University of Munich (TUM) and TUM University Hospital, Munich, Germany · School of Computation and Information Technology, Technical University of Munich, Munich, Germany · Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Neuherberg, Germany · Department of Radiology, Boston Children’s Hospital and Harvard Medical School, Boston, USA · Munich Center for Machine Learning, Technical University of Munich, Munich, Germany · GE HealthCare, Munich, Germany · School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom · Department of Computing, Imperial College London, London, United Kingdom
Accelerated cardiac cine MRI requires reconstructing spatiotemporal images from highly undersampled k-space data. Implicit neural representations (INRs) enable scan-specific reconstruction without large training datasets, but encode content implicitly in network weights without physically interpretable parameters. Gaussian primitives provide an explicit and geometrically interpretable alternative, but their spectra are confined near the k-space origin, limiting high-frequency representation. We propose Gabor primitives for MRI reconstruction, modulating each Gaussian envelope with a complex exponential to place its spectral support at an arbitrary k-space location, enabling efficient representation of both smooth structures and sharp boundaries. To exploit spatiotemporal redundancy in cardiac cine, we decompose per-primitive temporal variation into a low-rank geometry basis capturing cardiac motion and a signal-intensity basis modeling contrast changes. Experiments on cardiac cine data with Cartesian and radial trajectories show that Gabor primitives consistently outperform compressed sensing, Gaussian primitives, and hash-grid INR baselines, while providing a compact, continuous-resolution representation with physically meaningful parameters.
Figures & tables
Figure 1: Left: Gaussian vs. Gabor primitives in image space and k -space. A Gaussian’s spectral support is fixed at the k -space origin; a Gabor primitive shifts it to ξi via complex-exponential modulation, enabling more efficient frequency coverage. Right: Cardiac cine image is modeled as a mixture of time-varying Gabor primitives. Geometry parameters ( μ , s , θ , ξ ) and complex weights w are generated from low-rank geometry (blue) and intensity (orange) bases. Primitives are rasterized, passed through a multi-coil forward model, and fitted to acquired k -space data end-to-end.
Cartesian R=12
Cartesian R=16
Radial R≈23
Method
ρ↓
PSNR ↑
SSIM ↑
FSIM ↑
Time ↓
PSNR ↑
SSIM ↑
FSIM ↑
Time ↓
PSNR ↑
SSIM ↑
FSIM ↑
Time ↓
L+S [ 16 ]
—
37.15
0.940
0.850
0.3
32.19
0.824
0.777
0.4
35.82
0.922
0.810
1.5
PICS [ 14 ]
—
42.21
0.972
0.886
0.1
41.05
0.966
0.875
0.1
35.19
0.905
0.793
1.1
Hash-INR [ 15 ]
2.60
39.63
0.921
0.841
4.6
37.77
0.893
0.815
4.6
34.00
0.849
0.767
8.0
Gaussian
0.42
41.50
0.972
0.874
1.2
40.67
0.967
0.864
1.2
36.67
0.942
0.810
3.4
Gabor (ours)
0.41
42.61
0.974
0.883
2.5
41.39
0.968
0.871
2.5
37.53
0.947
0.830
4.2
Table 1: Quantitative comparison on cardiac cine MRI ( N=99 Cartesian, N=102 radial). PSNR in dB, Time in minutes. ρ=Nparams/(2HWT) : ratio of learnable parameters to real-valued image degrees of freedom. Best in bold , second best underlined .
Figure 2: Reconstruction comparison on Cartesian (top) and radial (bottom) cardiac cine. Each block shows a representative frame with metrics, zoomed ROI with error map, and y – t profile with temporal error.
Figure 3: Unique capabilities of Gabor primitives. (a) k -space primitive distribution: each dot is a primitive’s center frequency ξn with 3σ support ellipses. (b) Frequency-band PSNR (low, mid, high) on the radial dataset, averaged over all subjects. (c) Frequency decomposition: primitives partitioned by ∣ξn∣ into low- ( <41 ) and high-frequency ( ≥41 ) groups and their sum. (d) 4× super-resolution on the marked ROI; bicubic upsampling of the reference shown for comparison.
Reliable quantitative analysis of dynamic contrast-enhanced MRI requires high-quality spatiotemporal reconstructions at high undersampling rates. Scan-specific reconstructions using Gaussian and Gabor primitives have shown promising results without the need for large training datasets, but have not addressed the additional dimension of dynamic contrast. We propose a multi-dimensional, primitive based framework for dynamic contrast-enhanced MRI reconstruction that disentangles the underlying anatomy, the dynamic contrast enhancement, and residual motion into separate temporal basis functions, thereby enabling a geometrical interpretation of the representation. We show that this architecture achieves performance competitive with conventional reconstruction methods, both in reconstruction quality and in the accuracy of extracted aorta and kidney enhancement curves. The modular tier design extends naturally to additional dynamic factors and higher acceleration rates. Code available at https://github.com/compai-lab/2026-GaborDCE-spieker.
Veronika Spieker, Wenqi Huang, Cemre Ariyurek +5
Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Germany · School of Computation and Information Technology, Technical University of Munich, Germany · Department of Radiology, Boston Children’s Hospital and Harvard Medical School, USA +3
Cardiac cine Magnetic Resonance Imaging (MRI) is a critical diagnostic tool that provides dynamic insights for radiologists. To accelerate acquisition, under-sampled k-space data is often used, requiring reconstruction methods that combine coil sensitivity encoding with prior information to recover missing data. Deep learning approaches have gained more attention for leveraging data-adaptive priors. While supervised learning approaches are a common choice, they depend on fully sampled reference data, which is not always available. Unsupervised methods eliminate the need for fully sampled reference data, which can be advantageous in cardiac cine MRI reconstruction. Among them, implicit neural representations (INRs) have shown great potential due to their simple architecture and good quality reconstructions. In this work, we propose an image-domain dual-branch INR framework, termed I-FP-INR, which extends the original INR design by introducing an additional feature-processing branch. This design aims to extract complementary feature embeddings to enhance the overall representation, thereby benefiting reconstruction. Extensive evaluations on both public datasets and in-house data show consistent improvements over baseline methods in reconstruction quality, with strong robustness across varied scenarios.
Donghang Lyu, Marius Staring, Yiming Dong +3
Division of Image Processing, Department of Radiology, Leiden University Medical Center, 2333ZA Leiden, Netherlands · C.J. Gorter Center, Department of Radiology, Leiden University Medical Center, 2333ZA Leiden, Netherlands · Philips Innovative Technologies, 22335 Hamburg, Germany +1
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.
Yu Guan, Mingyu Hu, Jiale Hu +3
School of Advanced Manufacturing and the School of Information Engineering, Nanchang University, Nanchang 330031, China · Key Laboratory of Biomedical Imaging Science and System, Chinese Academy of Sciences, Shenzhen 518055, China · School of Information Engineering, Nanchang University, Nanchang 330031, China +1