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Complex sparse projections for compressed sensing

Moghadam A, Radha H ...see all

2010 44th Annual Conference on Information Sciences and Systems, CISS 2010 (2010)

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Abstract

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

Author-supplied keywords

  • Channel decoding
  • Compressed sensing
  • Sparse projections

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Authors

  • Abdolreza Abdolhosseini Moghadam

  • Hayder Radha

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