Abstract
Rank minimization problems, which consist of finding a matrix of minimum rank subject to linear constraints, have been proposed in many areas of engineering and science. A specific problem is the matrix completion problem in which a low rank data matrix is recovered from incomplete samples of its entries by solving a rank penalized least squares problem. The rank penalty is in fact the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm of the matrix singular values. A convex relaxation of this penalty is the commonly used l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm of the matrix singular values. In this paper we bridge the gap between these two penalties and propose a simple method for solving the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , q ∈ (0, 1), penalized least squares problem for matrix completion. We illustrate with simulations comparing our method to others in terms of solution quality.
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