Low density frames for compressive sensing

We consider the compressive sensing of a sparse or compressible signal x ∈ 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 even in the presence of additive noise. Low density frames are sparse matrices and have small storage requirements. Our decoding algorithms for these frames can be implemented in O(Md_vd_c) complexity, where d_c and d_v are the row and column weight of the frame respectively. Simulation results are provided, demonstrating that our approach significantly outperforms state-of-the-art recovery algorithms for numerous cases of interest.