On the Doubly Sparse Compressed Sensing Problem

Grigory Kabatiansky (1) , Cedric Tavernier (2) , Serge Vladuts (3, 1)

1 IITP - Dobrushin laboratory of Mathematics
2 Assystem France
3 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Informatique [cs]; Théorie de l'information [cs.IT]; Mathématiques [math]; Théorie de l'information et codage [math.IT]

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