Gabor primitives reconstruct accelerated cardiac cine MRI with higher PSNR than compressed sensing, Gaussian primitives, and hash-grid INR baselines on both Cartesian and radial trajectories

Introduces a complex-valued Gabor primitive formulation in which each primitive carries a freely positionable k-space spectral component, reducing to a standard Gaussian primitive when the modulation frequency ξn=0. Prior Gaussian primitives in MRI have spectra anchored at the k-space origin, so high-frequency content requires superposing many narrow Gaussians; Gabor modulation moves spectral support to arbitrary k-space locations, reducing spectral overlap. Analytical derivation: Eq. (1) and its Fourier transform in Eq. (2) show the k-space Gaussian blob centered at ξn rather than the origin; Fig. 3a shows learned ξn distributed across k-space, and Fig. 3b shows similar low-frequency PSNR across methods on the radial cohort while Gabor yields the largest gains in mid- and high-frequency bands.

Designs a two-component low-rank temporal model that splits per-primitive dynamics into a geometry basis capturing cardiac motion and an intensity basis modeling signal-intensity variations, with the weight matrix W of rank at most Rc+Rg. Rather than leaving temporal variation to network weights or hand-crafted regularizers, the model imposes a structured low-rank prior directly in primitive parameter space and explicitly separates geometry dynamics from contrast changes. Eq. (4) and Eq. (5) give the parameterization, and experiments use Rg=6, Rc=4 with geometry–contrast coupling; Fig. 2 y–t profiles show L+S blurs temporal motion boundaries while Gabor yields the lowest spatial and temporal error in both settings.

On cardiac cine MRI with Cartesian and radial trajectories at high acceleration, Gabor primitives outperform compressed sensing, Gaussian primitive, and hash-grid INR baselines in all evaluation settings. Prior frequency-modulated primitives were designed for non-negative real-valued signals and did not directly extend to the complex-valued MRI setting; this work applies Gabor primitives to complex-valued MRI with multi-trajectory validation. Table 1 covers N=99 Cartesian and N=102 radial data: Gabor has the highest PSNR and SSIM in all three settings, gains of +1.11/+0.72/+0.86 dB over Gaussian, and +2.34 dB over PICS on radial data; PICS is marginally higher on Cartesian FSIM; Hash-INR requires ρ=2.60 (about 6× more parameters) yet ranks last among learned methods.

Gabor primitives provide a compact, continuous-resolution representation with physically meaningful parameters, enabling spectral decomposition by |ξn| and 4× super-resolution without retraining. Grid-based methods and Gaussian primitives lack decomposition by modulation frequency (Gaussian has |ξn|=0), and the continuous representation supports evaluation at arbitrary resolution. Fig. 3c partitions primitives by |ξn|<1/4 and ≥1/4, with low-frequency primitives capturing smooth anatomy and high-frequency ones capturing edges; in Fig. 3d 4× super-resolution Gabor recovers sharper structures than Gaussian, while Hash-INR produces visible raster artifacts from overfitting the sampled grid; the parameter ratio ρ<0.5 is the most compact representation.

The result targets scan-specific cardiac cine MRI reconstruction: each acquisition is optimized individually, and it applies to highly accelerated undersampled settings with Cartesian and radial trajectories, with the authors reporting 2–4 minutes of optimization. The formulation is currently 2D, and the authors propose extending to 3D and joint spatiotemporal frequency modulation to improve temporal modeling. The explicit parameterization offers physical interpretability, such as spectral decomposition by modulation frequency, and could provide compact descriptors for downstream tasks such as motion quantification.

As a scan-specific method, each acquisition requires individual optimization of 2–4 minutes, which the authors identify as a remaining limitation. The formulation is currently 2D, and 3D plus joint spatiotemporal frequency modulation remain to be explored. The authors note that validation on additional anatomies and clinical diagnostic evaluation are needed for translation. Gabor is slower than Gaussian because it captures high frequencies via modulation rather than spatial narrowing, resulting in spatially wider primitives on average and more per-pixel overlap during rasterization. PICS is marginally higher on Cartesian FSIM, indicating that rankings are not fully consistent across metrics.