The restricted isometry property meets nonlinear approximation with redundant frames
نویسندگان
چکیده
منابع مشابه
Fusion Frames and the Restricted Isometry Property
We show that RIP frames, tight frames satisfying the restricted isometry property, give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We also show how to replace parts of the RIP frame with orthonormal sets while maintaining the restricted isometry property.
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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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The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some no...
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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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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2013
ISSN: 0021-9045
DOI: 10.1016/j.jat.2012.09.008