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.
The work of Grigory Kabatiansky and Serge Vlǎduţ was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150. The work of Cedric Tavernier was partially supported by SCISSOR ICT project no. 644425, funded by the European Commission Information & Communication Technologies H2020 Framework Program.
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Kabatiansky, G., Vlǎduţ, S., Tavernier, C. (2015). On the Doubly Sparse Compressed Sensing Problem. In: Groth, J. (eds) Cryptography and Coding. IMACC 2015. Lecture Notes in Computer Science(), vol 9496. Springer, Cham. https://doi.org/10.1007/978-3-319-27239-9_11
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DOI: https://doi.org/10.1007/978-3-319-27239-9_11
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