  Magnetic resonance imaging (MRI) is a powerful imaging modality that
revolutionizes medicine and biology. The imaging speed of high-dimensional MRI
is often limited, which constrains its practical utility. Recently, low-rank
tensor models have been exploited to enable fast MR imaging with sparse
sampling. Most existing methods use some pre-defined sampling design, and
active sensing has not been explored for low-rank tensor imaging. In this
paper, we introduce an active low-rank tensor model for fast MR imaging. We
propose an active sampling method based on a Query-by-Committee model, making
use of the benefits of low-rank tensor structure. Numerical experiments on a
3-D MRI data set demonstrate the effectiveness of the proposed method.
