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.

翻译：鼻音磁共振成像模式可以量化血动动力学,但需要较长的获取时间,不能广泛用于心血管疾病的早期诊断。为了缩短获取时间,经常使用从未得到充分抽样测量法的重建方法,这些方法可以发挥提高图像压缩作用。重新构建解剖和热感动图像可能会产生视觉文物。虽然其中一些工艺品基本上是重建错误,因此是取样不足的结果,但另一些可能是测量噪音或抽样频率随机选择的结果,否则,重建后的图像会变成随机变异,其偏向和共变都可能导致视觉文物;后者导致空间相关性,而视觉信息可能会被误解。虽然对前者的性质进行了研究,但后者没有引起太多的注意。在本研究中,我们调查了重建过程中随机扰动的理论属性,并对模拟和光学的频率进行了一些数字实验。我们的结果显示,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,在高压下,低压下,在高压下,在高压下,可能增加。