Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation

TL;DR

Motion in the abdomen induces artifacts in dynamic, motion-resolved MRI, challenging regularization when neural implicit k-space representations (NIK) are trained solely in k-space. The paper introduces PISCO, a GRAPPA-inspired, calibration-free self-consistency loss that enforces convergence of multiple weight sets derived from random k-space subsets, and integrates this into NIK training via a data-consistency loss $L_{DC}$ and a regularization loss $L_{PISCO}$. The approach is validated on simulated XCAT dynamics and in-vivo abdominal data, showing improved PSNR and FSIM, as well as smoother temporal evolution without sacrificing spatial detail, particularly at higher accelerations. These results demonstrate that calibration-free, k-space-based regularization can enhance high-temporal-resolution motion-resolved MRI and may generalize to other k-space reconstruction problems in clinical workflows.

Abstract

Neural implicit k-space representations have shown promising results for dynamic MRI at high temporal resolutions. Yet, their exclusive training in k-space limits the application of common image regularization methods to improve the final reconstruction. In this work, we introduce the concept of parallel imaging-inspired self-consistency (PISCO), which we incorporate as novel self-supervised k-space regularization enforcing a consistent neighborhood relationship. At no additional data cost, the proposed regularization significantly improves neural implicit k-space reconstructions on simulated data. Abdominal in-vivo reconstructions using PISCO result in enhanced spatio-temporal image quality compared to state-of-the-art methods. Code is available at https://github.com/vjspi/PISCO-NIK.

Figures (4)

• Figure 1: Overview. A: Multiple pairs of targets and surrounding neighbors $y_i^T, y_i^P$ are sampled and randomly sorted into subsets and solved for the linear relationship $W_s$ (Eq. \ref{['eq:PISCO_weightsolving']}). PISCO aims to minimize the distance between all $\mathrm{W_s}$. For simplicity, the coil dimension $N_c$ is not visualized, but included in matrix dimensions. B: PISCO for regularization of NIK. Any points can be sampled, but $L_{DC}$ can only be compared to measured k-space $y_{meas}$ (gray lines). $L_{PISCO}$ refines independent of $y_{meas}$.
• Figure 2: Quantitative results for 20 motion-affected simulation slices accelerated by R=1,2,3. All comparisons, except those marked with "N", are statistically significant (Wilcoxon signed rank test with False Discovery Rate correction at p$<$0.05).
• Figure 3: Static in-vivo reconstructions (thighs) for accelerations R=1,2,3. Exclusion of the temporal component enables comparison to INUFFT-R1, showing increased PSNR using PISCO regularization. PISCO-NIK sharpens reconstructions (blue arrows and increased FSIM) and reduces ringing artefacts of NIK-R2 (green arrows).
• Figure 4: Dynamic in-vivo reconstructions for two abdominal slices, with spatial $xy$-image (fixed $t$) and temporal $yt$-image (fixed $x$ at white dotted line). Complete reconstruction videos in Suppl. Fig. 2. Temporally resolved reconstructions are not available for the gated reference and limited for INUFFT4/XD-GRASP4 (blue arrows). XD-GRASP50 results in streaking, but more precise vessel structure, likely due to less motion blurring (white arrow). NIK enables improved temporal resolution, whereas PISCO additionally temporally smoothens (blue arrow) while maintaining spatial sharpness (white arrow).