English

Compressive Sensing Using Low Density Frames

Information Theory 2009-03-05 v1 math.IT Computation

Abstract

We consider the compressive sensing of a sparse or compressible signal xRM{\bf x} \in {\mathbb R}^M. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce an accurate estimate x^\hat{\bf x} even in the presence of additive noise. Low density frames are sparse matrices and have small storage requirements. Our decoding algorithms for these frames have O(M)O(M) complexity. Simulation results are provided, demonstrating that our approach significantly outperforms state-of-the-art recovery algorithms for numerous cases of interest. In particular, for Gaussian sparse signals and Gaussian noise, we are within 2 dB range of the theoretical lower bound in most cases.

Keywords

Cite

@article{arxiv.0903.0650,
  title  = {Compressive Sensing Using Low Density Frames},
  author = {Mehmet Akçakaya and Jinsoo Park and Vahid Tarokh},
  journal= {arXiv preprint arXiv:0903.0650},
  year   = {2009}
}

Comments

11 pages, 6 figures, Submitted to IEEE Transactions on Signal Processing

R2 v1 2026-06-21T12:18:03.444Z