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.
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)