Maximum entropy low-rank matrix recovery

We propose a novel, information-theoretic mask construction method, called MaxEnt, for efficient data acquisition for low-rank matrix recovery. Fundamental to this design approach is the maximum entropy principle, which states that the measurement masks which maximize the entropy of observations also maximize the information gain on the unknown matrix X. Coupled with a low-rank stochastic model for X, such a principle (i) reveals novel connections between information-theoretic sampling, compressive sensing and coding theory, and (ii) yields efficient mask construction algorithms for recovering X, which significantly outperform random measurements. We demonstrate the usefulness of MaxEnt in two real-world applications on image recovery and text document indexing.