As an acceleration technique for use with magnetic resonance imaging (MRI), compressed sensing MRI (CSMRI) was introduced recently to obtain MR images from undersampled k-space data. Images generated using a nonlinear iterative procedure based on sophisticated theory in informatics using data sparsity have complicated characteristics. Therefore, the factors affecting image quality (IQ) in CS-MRI must be elucidated. This article specifically describes the examination of the IQ of clinically important MR angiography (MRA). For MRA, the depictability of thin blood vessels is extremely important, but quantitative evaluation of thin blood vessel depictability is difficult. Therefore, we conducted numerical experiments using a simple numerical phantom model mimicking the cerebral arteries so that the experimental conditions, including the thin vessel positions, can be given. Results show that vessel depictability changed depending on the noise intensity when the wavelet transform was used as the sparsifying transform. Decreased vessel depictability might present difficulties at the clinical signal-to-noise ratio (SNR) level. Therefore, selecting data acquisition and reconstruction conditions carefully in terms of the SNR is crucially important for CS-MRI study.