80 research outputs found
Sharp RIP Bound for Sparse Signal and Low-Rank Matrix Recovery
This paper establishes a sharp condition on the restricted isometry property
(RIP) for both the sparse signal recovery and low-rank matrix recovery. It is
shown that if the measurement matrix satisfies the RIP condition
, then all -sparse signals can be recovered exactly
via the constrained minimization based on . Similarly, if
the linear map satisfies the RIP condition ,
then all matrices of rank at most can be recovered exactly via the
constrained nuclear norm minimization based on . Furthermore, in
both cases it is not possible to do so in general when the condition does not
hold. In addition, noisy cases are considered and oracle inequalities are given
under the sharp RIP condition.Comment: to appear in Applied and Computational Harmonic Analysis (2012
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