Complex sparse projections for compressed sensing
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 Â¿ 4k real measurements (where each\ncomplex sample is counted as two real measurements) suffice to recover\na k-sparse signal perfectly.