Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Genetic Algorithm based Orthogonal Matching Pursuit for Sparse Signal Recovery

희소 신호 복원을 위한 유전 알고리듬 기반 직교 정합 추구

  • Kim, Seehyun (Department of Information and Communications Engineering, The University of Suwon)
  • Received : 2014.07.31
  • Accepted : 2014.09.01
  • Published : 2014.09.30
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Abstract

In this paper, an orthogonal matching pursuit (OMP) method combined with genetic algorithm (GA), named GAOMP, is proposed for sparse signal recovery. Some recent greedy algorithms such as SP, CoSaMP, and gOMP improved the reconstruction performance by deleting unsuitable atoms at each iteration. However they still often fail to converge to the solution because the support set could not avoid the local minimum during the iterations. Mutating the candidate support set chosen by the OMP algorithm, GAOMP is able to escape from the local minimum and hence recovers the sparse signal. Experimental results show that GAOMP outperforms several OMP based algorithms and the $l_1$ optimization method in terms of exact reconstruction probability.

본 논문에서는 압축적으로 센싱된 희소 신호를 복원하기 위한 유전 알고리듬(GA)에 기반한 직교 정합 추구 방법(GAOMP)을 제안한다. 최근에 제안된 SP, CoSaMP, gOMP 등은 매 반복 단계에서 부적절한 atom을 제거하여 희소 신호의 복원 성능을 개선하였다. 그러나 support set이 국소 최저에 빠져 신호 복원에 실패하는 경우가 발생한다. 제안된 GAOMP는 유전 알고리듬의 중요 연산자인 변이를 통해 support set이 국소 최저를 벗어날 수 있도록 도와주어 희소 신호의 복원 성능을 향상시킨다. 모의 실험을 통해 GAOMP가 여러 OMP 기반 알고리듬과 $l_1$ 최적화보다 우수한 신호 복원 성능을 보임을 알 수 있다.

Keywords

References

  1. E. Candes, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans., Information Theory, vol. 52, no. 2, Feb. 2006, pp. 489-509. https://doi.org/10.1109/TIT.2005.862083
  2. D. Donoho, M. Elad, and V. Temlyakov, "Stable recovery of sparse overcomplete representation in the presence of noise," IEEE Trans., Information Theory, vol. 52, no. 1, Jan. 2006, pp. 6-18. https://doi.org/10.1109/TIT.2005.860430
  3. E. Candes and T. Tao, "Decoding by linear programming," IEEE Trans., Information Theory, vol. 51, no. 12, Dec. 2005, pp. 4203-4215. https://doi.org/10.1109/TIT.2005.858979
  4. S. Mallat and Z. Zhang, "Matching pursuit with time-frequency dictionaries," IEEE Trans., Signal Processing, vol. 41, no. 12, Dec. 1993, pp. 3397-3415. https://doi.org/10.1109/78.258082
  5. J. Tropp, "Greed is good: algorithmic results for sparse approximation," IEEE Trans., Information Theory, vol. 50, no. 10, Oct. 2004, pp. 2231-2242. https://doi.org/10.1109/TIT.2004.834793
  6. D. Donoho, et. al., "Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit," IEEE Trans., Information Theory, vol. 58, no. 2, Feb. 2012, pp. 1094-1121. https://doi.org/10.1109/TIT.2011.2173241
  7. D. Needell and J. Tropp, "Cosamp: Iterative signal recovery from incomplete and inaccurate samples," Applied and Computational Harnonic Analysis, vol. 26, no. 3, May 2009, pp. 301-321. 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., Information Theory, vol. 55, no. 5, Feb. 2009, pp. 2230-2249. https://doi.org/10.1109/TIT.2009.2016006
  9. J. Wang, S. Kwon, and B. Shim, "Generalized orthogonal matching pursuit," IEEE Trans., Signal Processing, vol. 60, no. 12, Dec. 2012, pp. 6202-6216. https://doi.org/10.1109/TSP.2012.2218810
  10. H. Huang and A. Makur, "Backtracking-based matching pursuit method for sparse signal reconstruction," IEEE Trans., Signal Processing Letters, vol. 18, no. 7, July 2011, pp. 391-394. https://doi.org/10.1109/LSP.2011.2147313
  11. M. Mitchell, An Introduction to Genetic Algorithms, MIT Press, 1996.
  12. http://sparselab.stanford.edu