منابع مشابه
Sparse Recovery Using Sparse Random Matrices
Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* t...
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For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by `1-minimization under the optimal condition m ≥ c s ln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes...
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In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AXB . The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard compressive sensing (CS) theory after converting it to vector form using the Kronecker operation. In this case, the measurement matrix assumes a Kronecker product stru...
متن کاملNonuniform Sparse Recovery with Gaussian Matrices
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as l1-minimization find the sparsest solution to certain systems of equations. Random matrices have become a popular choice for the measurement matrix. Indeed, near-optimal uniform recovery results have been shown for such matrices. In this note we f...
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ژورنال
عنوان ژورنال: Proceedings of the IEEE
سال: 2010
ISSN: 0018-9219,1558-2256
DOI: 10.1109/jproc.2010.2045092