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On the Doubly Sparse Compressed Sensing Problem
September 23, 2015 Β· Declared Dead Β· π IMA Conference on Cryptography and Coding
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Authors
Grigory Kabatiansky, Cedric Tavernier, Serge Vladuts
arXiv ID
1509.07145
Category
cs.IT: Information Theory
Citations
2
Venue
IMA Conference on Cryptography and Coding
Last Checked
4 months ago
Abstract
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to make 2(t+l) measurements, where t is the sparsity of original data. Moreover for this case a rather simple recovery algorithm is proposed. An analog of the Singleton bound from coding theory is derived what proves optimality of the corresponding measurement matrices.
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