  We propose in this paper a novel, information-theoretic method, called
MaxEnt, for efficient data acquisition for low-rank matrix recovery. This
proposed method has important applications to a wide range of problems,
including image processing and text document indexing. Fundamental to our
design approach is the so-called maximum entropy principle, which states that
the measurement masks which maximize the entropy of observations, also maximize
the information gain on the unknown matrix $\mathbf{X}$. Coupled with a
low-rank stochastic model for $\mathbf{X}$, such a principle (i) reveals novel
connections between information-theoretic sampling and subspace packings, and
(ii) yields efficient mask construction algorithms for matrix recovery, which
significantly outperforms random measurements. We illustrate the effectiveness
of MaxEnt in simulation experiments, and demonstrate its usefulness in two
real-world applications on image recovery and text document indexing.
