방송공학회논문지 (Journal of Broadcast Engineering)

  • 제17권6호
  • /
  • Pages.954-963
  • /
  • 2012
  • /
  • 1226-7953(pISSN)
  • /
  • 2287-9137(eISSN)
한국방송∙미디어공학회 (The Korean Institute of Broadcast and Media Engineers)
권호 표지
DOI QR코드

DOI QR Code

다중 후보 매칭 퍼슛

Multiple Candidate Matching Pursuit

  • 투고 : 2012.09.10
  • 심사 : 2012.11.23
  • 발행 : 2012.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Orthogonal matching pursuit (OMP) 알고리듬은 underdetermined 시스템에서 희소 신호를 복구하는 대표적인 greedy 알고리듬으로 많은 관심을 받고 있다. 본 논문에서는 OMP 알고리듬의 반복과정에서 후보 support 집합들을 구성하여 마지막 반복과정에서 최소 잔차를 이용하는 multiple candidate matching pursuit (MuCaMP) 기법을 제안한다. MuCaMP 가 완벽한 신호 복원을 보장하기 위한 restricted isometry property (RIP)를 이용한 충분조건, ${\delta}_{N+K}<\frac{\sqrt{N}}{\sqrt{K}+3\sqrt{N}}$을 제시한다. 실험을 통해 후보 support 집합들의 크기에 따른 성능과 MuCaMP의 복원 성능이 기존의 기법들에 비해 우수함을 확인하였다.

As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention. In this paper, we multiple candidate matching pursuit (MuCaMP), which builds up candidate support set in every iteration and uses the minimum residual at last iteration. Using the restricted isometry property (RIP), we derive the sufficient condition for MuCaMP to recover the sparse signal exactly. The MuCaMP guarantees to reconstruct the K-sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{N+K}<\frac{\sqrt{N}}{\sqrt{K}+3\sqrt{N}}$. In addition, we show a recovery performance both noiseless and noisy measurements.

키워드

과제정보

연구 과제 주관 기관 : 방송통신위원회

참고문헌

  1. D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM Journal on Applied Mathematics, Vol. 49, no. 3, pp. 906-931, 1989 https://doi.org/10.1137/0149053
  2. R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approximation, Vol. 28, no. 3, pp. 253-263, Dec. 2008 https://doi.org/10.1007/s00365-007-9003-x
  3. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Information Theory, Vol. 52, no. 2, pp. 489-509, Feb. 2006 https://doi.org/10.1109/TIT.2005.862083
  4. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans. on Information Theory, Vol. 51, no. 12, pp. 4203-4215, Dec. 2005 https://doi.org/10.1109/TIT.2005.858979
  5. R. Giryes and M. Elad, "RIP-Based Near-Oracle Performance Guarantees for SP, CoSaMP, and IHT," IEEE Trans. on Signal Processing, Vol. PP, no. 99, Nov. 2011
  6. J. A. Tropp and A. C. Gilbery, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. on Information Theory, Vol. 53, no. 12, pp. 4655-4666, Dec. 2007 https://doi.org/10.1109/TIT.2007.909108
  7. D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harmonic Analysis, Vol. 26, no. 3, pp. 301-321, Mar. 2009 https://doi.org/10.1016/j.acha.2008.07.002
  8. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. on Information Theory, Vol. 55, no. 5, pp. 2230-2249, May. 2009 https://doi.org/10.1109/TIT.2009.2016006
  9. D. Needell and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE J. Sel. Topics Signal Processing, Vol. 4, no. 2, pp. 310-316, Apr. 2010 https://doi.org/10.1109/JSTSP.2010.2042412
  10. D. L. Donoho and I. Drori and Y. Tsaig and J. L. Starck,, "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," Mar. 2006
  11. M. A. Davenport and M. B. Wakin, "Analysis of Orthogonal Matching Pursuit using the restricted isometry property," IEEE Trans. on Information Theory, Vol. 56, no. 9, pp. 4395-4401, Sep. 2010 https://doi.org/10.1109/TIT.2010.2054653
  12. E. J. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, Vol. 346, no. 9-10, pp. 589-592, May. 2008 https://doi.org/10.1016/j.crma.2008.03.014
  13. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. on Information Theory, Vol. 50, no. 10, pp. 2231-2242, Oct. 2004 https://doi.org/10.1109/TIT.2004.834793

피인용 문헌

  1. Rate Allocation for Block-based Compressive Sensing vol.20, pp.3, 2015, https://doi.org/10.5909/JBE.2015.20.3.398