An analysis of reconstruction noise from undersampled 4D flow MRI

TL;DR

This paper investigates the statistical properties of noise and artifacts in undersampled 4D flow MRI reconstructions, revealing how different sampling patterns and reconstruction methods influence artifact correlation lengths.

Contribution

It provides a theoretical analysis of the random perturbations in MRI reconstruction, highlighting how undersampling patterns affect artifact correlations and image quality.

Findings

Correlation length limited to 2-3 pixels with Gaussian sampling and $\\ell_1$-norm recovery

Correlation length increases with other sampling patterns and higher undersampling factors

Numerical experiments on simulated and real MR aortic flow validate theoretical insights

Abstract

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce the acquisition times, reconstruction methods from undersampled measurements are routinely used, that leverage representations designed to increase image compressibility. Reconstructed anatomical and hemodynamic images may present visual artifacts. Although some of these artifact are essentially reconstruction errors, and thus a consequence of undersampling, others may be due to measurement noise or the random choice of the sampled frequencies. Said otherwise, a reconstructed image becomes a random variable, and both its bias and its covariance can lead to visual artifacts; the latter leads to spatial correlations that may be misconstrued for visual information. Although the nature of the former has been studied in the literature, the latter has not received as much attention. In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process, and perform a number of numerical experiments on simulated and MR aortic flow. Our results show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with recovery algorithms based on $\ell_1$-norm minimization. However, the correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., 8x or 16x compression), and different reconstruction methods.