Restricted Isometry Property for General p-Norms
نویسندگان
چکیده
منابع مشابه
A Generalized Restricted Isometry Property
Compressive Sampling (CS) describes a method for reconstructing high-dimensional sparse signals from a small number of linear measurements. Fundamental to the success of CS is the existence of special measurement matrices which satisfy the so-called Restricted Isometry Property (RIP). In essence, a matrix satisfying RIP is such that the lengths of all sufficiently sparse vectors are approximate...
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Given a matrix A with n rows, a number k < n, and 0 < δ < 1, A is (k, δ)-RIP (Restricted Isometry Property) if, for any vector x ∈ R, with at most k non-zero co-ordinates, (1− δ)‖x‖2 ≤ ‖Ax‖2 ≤ (1 + δ)‖x‖2 In other words, a matrix A is (k, δ)-RIP if Ax preserves the length of x when x is a k-sparse vector. In many applications, such as compressed sensing and sparse recovery, it is desirable to c...
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Let A be a matrix whose columns X1, . . . , XN are independent random vectors in R. Assume that p-th moments of 〈Xi, a〉, a ∈ Sn−1, i ≤ N , are uniformly bounded. For p > 4 we prove that with high probability A has the Restricted Isometry Property (RIP) provided that Euclidean norms |Xi| are concentrated around √ n and that the covariance matrix is well approximated by the empirical covariance m...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2016
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2016.2598296