Online performance guarantees for sparse recovery

8 years 11 months ago
Online performance guarantees for sparse recovery
A K∗ -sparse vector x∗ ∈ RN produces measurements via linear dimensionality reduction as u = Φx∗ + n, where Φ ∈ RM×N (M < N), and n ∈ RM consists of independent and identically distributed, zero mean Gaussian entries with variance σ2 . An algorithm, after its execution, determines a vector ˆx that has K-nonzero entries, and satisfies u − Φˆx ≤ . How far can ˆx be from x∗ ? When the measurement matrix Φ provides stable embedding to 2Ksparse signals (the so-called restricted isometry property), they must be very close. This paper therefore establishes worst-case bounds to characterize the distance ˆx − x∗ based on the online metainformation. These bounds improve the pre-run algorithmic recovery guarantees, and are quite useful in exploring various data error and solution sparsity trade-offs. We also evaluate the performance of some sparse recovery algorithms in the context of our bound.
Raja Giryes, Volkan Cevher
Added 21 Aug 2011
Updated 21 Aug 2011
Type Journal
Year 2011
Authors Raja Giryes, Volkan Cevher
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