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Gabor Primitives for Accelerated Cardiac Cine MRI Reconstruction
Wenqi Huang, Veronika Spieker, Nil Stolt-Ansó, Natascha Niessen, Maik Dannecker, Sevgi Gokce Kafali, Sila Kurugol, Julia A. Schnabel, Daniel Rueckert
TL;DR
Accelerated cardiac cine MRI must reconstruct high-resolution spatiotemporal images from undersampled data, while current scan-specific and explicit representations retain important limitations. This paper introduces Gabor primitives with freely positioned spectral support and a low-rank geometry–intensity temporal model. Across Cartesian and radial cardiac cine settings, Gabor primitives consistently outperform the evaluated baselines while retaining compact, physically interpretable parameters.
Problem
Undersampled cardiac cine MRI reconstruction needs effective priors, while INRs lack physical interpretability and Gaussian primitives have spectra confined near the k-space origin.
Method
The method modulates Gaussian envelopes with complex exponentials and models temporal variation using separate low-rank geometry and intensity bases.
Results
Gabor primitives consistently outperform compressed sensing, Gaussian primitive, and hash-grid INR baselines across Cartesian and radial cardiac cine settings.
Takeaways & Limitations
The representation provides compact, continuous-resolution cardiac cine reconstruction with physically meaningful spectral and temporal parameters.
Takeaways & Limitations
Each scan requires individual optimization taking 2–4 minutes, and the current formulation is limited to 2D with validation still needed on additional anatomies and clinical diagnosis.
Abstract
from arXiv · showhide
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.
1 Introduction
Accelerated cardiac cine MRI is an ill-posed undersampled reconstruction problem, while existing approaches trade off patient-specific detail, training-data requirements, hallucination risk, or physical interpretability. Gabor primitives address these limitations by shifting spectral support to arbitrary k-space locations and combining this with structured temporal modeling.
- 1 Introduction: Cardiac cine MRI must recover high spatial and temporal resolution from undersampled k-space, creating an ill-posed inverse problem that requires effective priors or regularization.
- 1 Introduction: Existing methods face complementary limitations: handcrafted regularizers may miss complex motion and detail, supervised models require large datasets and risk hallucination, and INRs lack physically interpretable parameters.
- 1 Introduction: Gabor primitives modulate Gaussian envelopes to place each primitive’s spectral component freely in k-space, efficiently representing smooth anatomy and sharp boundaries.Standard Gaussian primitives remain centered at the k-space origin, making high-frequency content costly to represent through many narrow primitives.
- 1 Introduction: The framework uses a two-component low-rank temporal model that separates per-primitive geometry dynamics from signal-intensity variations.
- 1 Introduction: Across cardiac cine datasets with Cartesian and radial trajectories at high acceleration, the method consistently improves over compressed sensing, Gaussian primitives, and hash-grid INR baselines.
2 Methods
The method represents cardiac cine MRI as spatiotemporally varying Gabor primitives whose modulation frequencies position spectral support away from the k-space origin. A structured low-rank temporal model separates geometry dynamics from intensity variations, and the resulting primitives are mapped through coil sensitivities and the acquisition trajectory.
- 2.1 Gabor Primitive Basis: Gabor primitives modulate Gaussian envelopes with complex exponentials, placing each primitive’s spectral support at an arbitrary k-space location rather than forcing it near the origin.The spectral component retains the Gaussian envelope’s orientation with reciprocal widths, while zero modulation recovers a standard Gaussian.
- 2.2 Spatiotemporal Forward Model: Each cine frame is modeled as a sum of N Gabor primitives whose weights and geometry vary across time.The primitive parameters include frame-dependent centers, scales, orientations, modulation frequencies, and complex weights.
- 2.2 Spatiotemporal Forward Model: A shared low-rank geometry basis captures cardiac motion, with per-primitive coefficient matrices controlling how each primitive couples to the motion basis.Geometric parameters are represented as static components plus low-rank perturbations from the shared temporal basis.
- 2.2 Spatiotemporal Forward Model: An independent intensity basis models signal variations, while geometry coupling captures motion-induced effects such as partial-volume and flow changes.The resulting weight matrix has rank at most R_c + R_g, imposing low-rank temporal structure directly in primitive parameter space.
- 2.2 Spatiotemporal Forward Model: Predicted images are converted to multi-coil k-space by applying coil sensitivity maps and a trajectory-specific Fourier operator before joint optimization.The implementation rasterizes frame-specific primitives, multiplies by coil sensitivities, and uses a masked FFT for Cartesian or NUFFT for non-Cartesian sampling; training combines data fidelity, weight sparsity, and temporal total variation.
3 Experiments
The experiments evaluate Gabor primitives against conventional reconstruction methods and scan-specific learned representations on Cartesian and radial cardiac cine MRI.
- Datasets: Evaluation uses 99 Cartesian and 102 radial cardiac cine acquisitions, with Cartesian data retrospectively undersampled at R=12 and R=16 and radial data at R≈23.Cartesian references contain approximately 19 frames and 15–18 coils; radial references contain 25 cardiac phases with 8 compressed coils.
- Baselines: Baselines comprise L+S, PICS, Hash-INR, and Gaussian primitives, with Gaussian primitives serving as the ξn ≡0 ablation.L+S uses robust PCA, PICS combines parallel imaging and total variation, and Hash-INR uses multi-resolution hash-grid encoding.
- Implementation: Gabor and Gaussian models use matched parameter-count settings, temporal ranks Rg=6 and Rc=4, adaptive density control, and 5,000 training iterations.Both primitive methods use geometry–contrast coupling and the same regularization coefficients λs=10−5 and λt=10−2.
4 Results
Gabor primitives achieve the strongest reconstruction quality across Cartesian and radial settings while retaining compact, continuous, and frequency-interpretable representations.
- Quantitative Comparison: Gabor primitives achieve the highest PSNR and SSIM across all three settings, with gains over Gaussian of +1.11, +0.72, and +0.86 dB.They also outperform all competitors on radial data at R≈23, including a +2.34 dB gain over PICS, while maintaining ρ<0.5.
- Quantitative Comparison: Gabor reconstruction is slower than Gaussian because wider spatial primitives overlap more per pixel during rasterization.This computational trade-off results from representing high frequencies through modulation rather than spatial narrowing.
- Qualitative Comparison: Gabor yields the lowest spatial and temporal error across Cartesian and radial reconstructions, whereas non-Gabor methods degrade more on radial data.Gaussian exhibits elevated tissue-boundary error under high acceleration, while voxel-based methods show background noise in error maps.
- Representation Properties: Gabor center frequencies distribute across k-space, producing the largest mid- and high-frequency PSNR gains while matching other methods at low frequencies.Gaussian primitives remain anchored at the k-space origin.
- Representation Properties: Partitioning primitives by |ξn| separates smooth anatomy into low-frequency components and edges into high-frequency components.Gaussian primitives have |ξn|=0 and therefore lack this frequency-based decomposition.
- Representation Properties: Gabor primitives support arbitrary-resolution evaluation without retraining and recover sharper structures than Gaussian primitives in 4× super-resolution.Hash-INR produces raster artifacts at increased resolution because it lacks inherent spatial continuity and can overfit the sampled grid.
5 Discussion and Conclusion
The paper concludes that Gabor primitives combine freely positioned spectral components with structured low-rank temporal modeling for compact, interpretable cardiac cine reconstruction.
- Discussion and Conclusion: Complex exponential modulation gives each primitive a freely positionable k-space component, enabling efficient high-frequency coverage beyond Gaussian primitives.The explicit parameterization supports physical interpretation through spectral decomposition by modulation frequency.
- Discussion and Conclusion: A two-component temporal model factorizes per-primitive dynamics into geometry and intensity bases, imposing a structured low-rank prior in primitive parameter space.The approach consistently outperforms baselines across cardiac cine settings with Cartesian and radial trajectories.
- Limitations: Each scan requires individual optimization taking 2–4 minutes, and the current formulation operates only in 2D.The authors also identify extension to 3D and additional anatomy and clinical validation as remaining needs.