Note on Sparsity in Signal Recovery and in Matrix Identification
نویسندگان
چکیده
منابع مشابه
Note on sparsity in signal recovery and in matrix identification
The standard approach to recover a signal with a sparse representation in D is to design a measurement matrix ΦD ∈ Cm×n which allows the recovery of any f ∈ Σk from the measurement vector ΦDf whenever k is sufficiently small. While a minimal requirement for the recovery of any f ∈ Σk is that the constructed map ΦD : Σ D k −→ C, f 7→ ΦDf is injective, the recent literature on sparse signal recov...
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Definition 1 (Restricted isometry and orthogonality). The S-restricted isometry constant δS of a matrix F ∈ Rn×m is the smallest quantity such that (1− δS)‖x‖2 ≤ ‖FTx‖2 ≤ (1 + δS)‖x‖2 for all T ⊆ [m] with |T | ≤ S and all x ∈ R|T |. The (S, S′)-restricted orthogonality constant θS,S′ of F is the smallest quantity such that |FTx · FT ′x′| ≤ θS,S′‖c‖‖c‖ for all disjoint T, T ′ ⊆ [m] with |T | ≤ S...
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Sparsity Pattern Recovery in Bernoulli-Gaussian Signal Model
In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery problem. The aim is to identify the non-zero elements in the original sparse signal. In this article we consider the sparsity pattern recovery problem under a p...
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ژورنال
عنوان ژورنال: The Open Applied Mathematics Journal
سال: 2007
ISSN: 1874-1142
DOI: 10.2174/1874114200701010021