Skip to content

Complex sparse projections for compressed sensing

by Abdolreza Abdolhosseini Moghadam, Hayder Radha
2010 44th Annual Conference on Information Sciences and Systems, CISS 2010 ()
Get full text at journal


Sparse projections for compressed sensing have been receiving some\nattention recently. In this paper, we consider the problem of recovering\na k-sparse signal (x) in an n-dimensional space from a limited number\n(m) of linear, noiseless compressive samples (y) using complex sparse\nprojections. Our approach is based on constructing complex sparse\nprojections using strategies rooted in combinatorial design and expander\ngraphs. We are able to recover the non-zero coefficients of the k-sparse\nsignal (x) iteratively using a low-complexity algorithm that is reminiscent\nof well-known iterative channel decoding methods. We show that the\nproposed framework is optimal in terms of sample requirements for\nsignal recovery (m = O (k log(n/k))) and has a decoding complexity\nof O (m log(n/m)), which represents a tangible improvement over recent\nsolvers. Moreover we prove that using the proposed complex-sparse\nframework, on average 2k lt; m ¿ 4k real measurements (where each\ncomplex sample is counted as two real measurements) suffice to recover\na k-sparse signal perfectly.

Cite this document (BETA)

Readership Statistics

11 Readers on Mendeley
by Discipline
55% Computer Science
45% Engineering
by Academic Status
45% Student > Ph. D. Student
18% Researcher
18% Student > Doctoral Student
by Country
9% Denmark

Sign up today - FREE

Mendeley saves you time finding and organizing research. Learn more

  • All your research in one place
  • Add and import papers easily
  • Access it anywhere, anytime

Start using Mendeley in seconds!

Sign up & Download

Already have an account? Sign in