An analysis of reconstruction noise from undersampled 4D flow MRI

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 acquisition times, flow reconstruction from undersampled data is routinely performed. Reconstructed anatomical and hemodynamic images may present visual artifacts. While some artifacts are reconstruction errors, and a consequence of undersampling, others are due to measurement noise or the random choice of samples. A reconstructed image becomes thus a random variable: its bias leads to systematic reconstruction errors, whereas its fluctuations may induce spatial correlations that may be misconstrued for visual information or that may carry to quantities of interest computed from the image. Although 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. To our knowledge, this is the first study on this topic. We perform numerical experiments on simulated flow, on aortic phantom flow, and on aortic flow. These show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with l(1)-norm minimization methods. The correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., higher than 8x compression), and other reconstruction methods. Our findings suggest that the reconstruction method has a large impact on the correlation. As reconstruction methods are routinely used in practice, the impact of these random perturbations in practical applications merits further study.