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Deterministic construction of binary, bipolar, and ternary compressed sensing matrices

Amini, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1109/TIT.2011.2111670
  3. Publisher: 2011
  4. Abstract:
  5. In this paper, we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar m × n RIP fulfilling ± 1 matrices of order k such that m ≤ script O sign (k(log2 n) log2 k/ln log2 k). The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ({0,1,-1} elements) that satisfy the RIP condition
  6. Keywords:
  7. Orthogonal optical codes (OOC) ; BCH code ; Compressed sensing ; Deterministic matrices ; Optical codes ; Restricted isometry property ; Algorithms ; Computational complexity ; Matrix algebra ; Signal reconstruction
  8. Source: IEEE Transactions on Information Theory ; Volume 57, Issue 4 , April , 2011 , Pages 2360-2370 ; 00189448 (ISSN)
  9. URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5730553