On the Doubly Sparse Compressed Sensing Problem

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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https://hal.archives-ouvertes.fr/hal-01218678
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Submitted on : Wednesday, October 21, 2015 - 3:48:35 PM
Last modification on : Monday, March 4, 2019 - 2:04:19 PM

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  • HAL Id : hal-01218678, version 1
  • ARXIV : 1509.07145

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Grigory Kabatiansky, Cedric Tavernier, Serge Vladuts. On the Doubly Sparse Compressed Sensing Problem. 2015. ⟨hal-01218678⟩

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