%0 Unpublished work
%T On the Doubly Sparse Compressed Sensing Problem
%+ Dobrushin laboratory of Mathematics (IITP)
%+ Assystem France
%+ Institut de MathÃ©matiques de Marseille (I2M)
%A Kabatiansky, Grigory
%A Tavernier, Cedric
%A Vladuts, Serge
%Z 6 pages, IMACC2015 (accepted)
%8 2015-09-23
%D 2015
%Z 1509.07145
%Z Computer Science [cs]
%Z Computer Science [cs]/Information Theory [cs.IT]
%Z Mathematics [math]
%Z Mathematics [math]/Information Theory [math.IT]Preprints, Working Papers, ...
%X 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.
%G English
%L hal-01218678
%U https://hal.archives-ouvertes.fr/hal-01218678
%~ CNRS
%~ EC-MARSEILLE
%~ INSMI
%~ I2M-2014-
%~ I2M
%~ UNIV-AMU
%~ TEST-AMU