Fourier Shell Analysis: k-Space-Based Metrics for Assessing Super-Resolution in 4D Flow MRI

To support the emerging field of super-resolution (SR) in 4D flow MRI by proposing Fourier shell analysis to disentangle resolution enhancement from denoising effects during evaluation.

A thoracic aortic 4D flow MRI dataset was synthesized with various degrees of stenosis, providing ground truth flow fields generated using computational fluid dynamics and MRI-specific downsampling to generate paired low- and high resolution (LR/HR) 4D Flow MRI data. To address potential confounding of resolution enhancement versus denoising effects when using current image-based error metrics, a k-space-based Fourier shell analysis is proposed to compare SR results to HR references using multiple concentric shells with increasing spatial frequency radii in k-space. To demonstrate its value, the performance of a deep learning SR network (4DFlowNet) with two degrees of transfer learning is compared for three different signal-to-noise ratios (SNR) of $\infty$ , 20, and 5.

It is demonstrated that Fourier shell analysis is superior in isolating and quantifying resolution enhancement compared to image-based metrics. When comparing SR performance of 4DFlowNet with different degrees of transfer learning, Fourier shell analysis isolates resolution enhancement more clearly relative to image-based normalized root-mean-square-error analysis (absolute relative mean paired difference of 160.3% vs. 13.1% for noiseless data, 92.3% vs. 12.4% for SNR of 20, and 300.0% vs. 10.2% for SNR of 5, respectively).

Fourier shell analysis allows for disentangling and quantifying resolution gain and denoising of SR methods in 4D flow MRI and should serve as an additional metric when assessing SR approaches.