Maximum entropy low-rank matrix recovery
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We propose a novel, information-theoretic method, called MaxEnt, for efficient data requisition for low-rank matrix recovery. This proposed method has important applications to a wide range of problems in image processing, text document indexing and system identification, and is particularly effective when the desired matrix X is high-dimensional, and measurements from X are expensive to obtain. Fundamental to this 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 X. Coupled with a low-rank stochastic model for X, such a principle (i) reveals several insightful connections between information-theoretic sampling, compressive sensing and coding theory, and (ii) yields efficient algorithms for constructing initial and adaptive masks for recovering X, which significantly outperforms random measurements. We illustrate the effectiveness of MaxEnt using several simulation experiments, and demonstrate its usefulness in two real-world applications on image recovery and text document indexing.
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