Optimal Exploitation of Subspace Prior Information in Matrix Sensing
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Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem and seismic data interpolation, there exists some prior information about the column and row spaces of the true low rank matrix. In this paper, we exploit this prior information by proposing a weighted optimization problem where its objective function promotes both rank and prior subspace information. Using the recent results in conic integral geometry, we obtain the unique optimal weights that minimize the required number of measurements. As simulation results confirm, the proposed convex program with optimal weights substantially needs fewer measurements than the regular nuclear norm minimization.
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