The Stability of Low-Rank Matrix Reconstruction: a Constrained Singular Value View

Details The Stability of Low-Rank Matrix Reconstruction: a Constrained Singular Value View The Stability of Low-Rank Matrix Reconstruction: a Constrained Singular Value View

2010-06-21

arxiv.org/abs/1006.4088v1

Computer Science

Information Theory

Submitted to IEEE Trans. Information Theory

Scientific paper

The stability of low-rank matrix reconstruction is investigated in this paper. The $\ell_*$-constrained minimal singular value ($\ell_*$-CMSV) of the measurement operator is shown to determine the recovery performance of nuclear norm minimization based algorithms. Compared with the stability results using the matrix restricted isometry constant, the performance bounds established using $\ell_*$-CMSV are more concise and tight, and their derivations are less complex. The computationally amenable $\ell_*$-CMSV and its associated error bounds also have more transparent relationships with the Signal-to-Noise Ratio. Several random measurement ensembles are shown to have $\ell_*$-CMSVs bounded away from zero with high probability, as long as the number of measurements is relatively large.

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