English

On the Doubly Sparse Compressed Sensing Problem

Information Theory 2015-09-25 v1 math.IT

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.

Keywords

Cite

@article{arxiv.1509.07145,
  title  = {On the Doubly Sparse Compressed Sensing Problem},
  author = {Grigory Kabatiansky and Cedric Tavernier and Serge Vladuts},
  journal= {arXiv preprint arXiv:1509.07145},
  year   = {2015}
}

Comments

6 pages, IMACC2015 (accepted)

R2 v1 2026-06-22T11:04:01.979Z