TY - GEN

T1 - General constructions of deterministic (S)RIP matrices for compressive sampling

AU - Mazumdar, Arya

AU - Barg, Alexander

PY - 2011

Y1 - 2011

N2 - Compressive sampling is a technique of recovering sparse N-dimensional signals from low-dimensional sketches, i.e., their linear images in ℝm, m ≪ N. The main question associated with this technique is construction of linear operators that allow faithful recovery of the signal from its sketch. The most frequently used sufficient condition for robust recovery is the near-isometry property of the operator when restricted to k-sparse signals. We study 1-matrices of dimensions m × N that satisfy the restricted isometry property of order k (k-RIP). As our main set of results, we describe a general method of constructing sampling matrices for which a statistical version of k-RIP holds. We also show that mN matrices with k-RIP and m = O(k2 logN) can be constructed with time complexity O(k 2N logN).

AB - Compressive sampling is a technique of recovering sparse N-dimensional signals from low-dimensional sketches, i.e., their linear images in ℝm, m ≪ N. The main question associated with this technique is construction of linear operators that allow faithful recovery of the signal from its sketch. The most frequently used sufficient condition for robust recovery is the near-isometry property of the operator when restricted to k-sparse signals. We study 1-matrices of dimensions m × N that satisfy the restricted isometry property of order k (k-RIP). As our main set of results, we describe a general method of constructing sampling matrices for which a statistical version of k-RIP holds. We also show that mN matrices with k-RIP and m = O(k2 logN) can be constructed with time complexity O(k 2N logN).

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U2 - 10.1109/ISIT.2011.6034217

DO - 10.1109/ISIT.2011.6034217

M3 - Conference contribution

AN - SCOPUS:80054816649

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 678

EP - 682

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -