Journal of Broadcast Engineering (방송공학회논문지)

The Korean Institute of Broadcast and Media Engineers (한국방송∙미디어공학회)
권호 표지
DOI QR코드

DOI QR Code

Convergence Complexity Reduction for Block-based Compressive Sensing Reconstruction

블록기반 압축센싱 복원을 위한 수렴 복잡도 저감

  • Park, Younggyun (Sungkyunkwan University, College of Information & Communication Engineering) ;
  • Shim, Hiuk Jae (Sungkyunkwan University, College of Information & Communication Engineering) ;
  • Jeon, Byeungwoo (Sungkyunkwan University, College of Information & Communication Engineering)
  • 박영균 (성균관대학교 정보통신대학) ;
  • 심혁재 (성균관대학교 정보통신대학) ;
  • 전병우 (성균관대학교 정보통신대학)
  • Received : 2014.02.10
  • Accepted : 2014.03.03
  • Published : 2014.03.30
Download PDF
⟨ Previous Next ⟩

Abstract

According to the compressive sensing theory, it is possible to perfectly reconstruct a signal only with a fewer number of measurements than the Nyquist sampling rate if the signal is a sparse signal which satisfies a few related conditions. From practical viewpoint for image applications, it is important to reduce its computational complexity and memory burden required in reconstruction. In this regard, a Block-based Compressive Sensing (BCS) scheme with Smooth Projected Landweber (BCS-SPL) has been already introduced. However, it still has the computational complexity problem in reconstruction. In this paper, we propose a method which modifies its stopping criterion, tolerance, and convergence control to make it converge faster. Experimental results show that the proposed method requires less iterations but achieves better quality of reconstructed image than the conventional BCS-SPL.

압축센싱 이론에 따르면 표본화 될 신호가 일련의 조건을 만족하는 성긴 신호라면 나이퀴스트 표본화주파수보다 적은 수의 측정 샘플들만 가지고도 원 신호를 완벽하게 복원할 수 있다. 그러나 압축센싱 이론을 실제 영상에 활용하기 위해서는, 신호 복원에 필요한 계산 복잡도와 메모리 요구량을 줄일 필요가 있다. 이런 관점에서 블록압축센싱(Block-based Compressive Sensing)에 기반한 Smooth Projected Landweber (BCS-SPL) 방법이 개발되었지만, 이 또한 복원과정의 계산 복잡도가 여전히 큰 문제가 있다. 본 논문에서는 기존의 BCS-SPL 복원 알고리즘의 수렴을 보다 빠르게 하기 위하여, 반복복원 중지조건, 허용 오차, 수렴 조절 인자를 개선한 수렴 복잡도 저감 방법을 제시한다. 제시한 방법은 기존 BCS-SPL 방법보다 낮은 수의 반복복원 횟수내로 수렴하면서도 동시에 복원 화질도 개선시키는 실험 결과를 보였다.

Keywords

References

  1. D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006. https://doi.org/10.1109/TIT.2006.871582
  2. E. J. Candes and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Mag., vol. 21, no. 3, pp. 21-30, Mar. 2008.
  3. E. J. Candes, J Romberg, and T Tao, "Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Info. Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006. https://doi.org/10.1109/TIT.2005.862083
  4. L. N. Smith, "How to find real-world applications for compressive sensing," in Proc. of SPIE Defense, Security and Sensing. Int. Society for Optics and Photonics, pp.87170Q-81170Q-10, May. 2013.
  5. Dharmpal Takhar, Jason N. Laska, Michael B. Wakin, Marco F. Duarte, Dror Baron, and et al., "A new compressive imaging camera architecture using optical-domain compression", in Proc. SPIE 6065, Computational Imaging IV, 606509, Feb. 2006.
  6. C. Eldar and G. Kutyniok, Compressed sensing: Theory and applications, Cambridge University Press, Jun. 2012.
  7. M. Fornasier and H. Rauhut, "Compressive Sensing," in Handbook of Mathematical Methods in Imaging, Springer, Heigelberg, Germany, 2011.
  8. L. Gan, "Block compressed sensing of natural images," in Proc. of International Conference on Digital Signal Processing, pp. 403-406, Jul. 2007.
  9. A. Tavakoli and A. Pourmohammad, "An efficient iterative thresholding method for compressed sensing," Int. Journal of Comuter Theory and Engineering, vol. 4, no. 2, pp. 270-273, April, 2012.
  10. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE Journal on Selected Areas in Comm., vol. 1, no. 4, pp. 586-597, Dec. 2007.
  11. S. A. Razavi, E. Ollila, and V. Koivunen, "Robust greedy algorithms for compressed sensing," in Proc. IEEE Conf., European Signal Processing, pp. 969-973, Aug. 2012.
  12. S. Mun and J. E. Fowler, "Block compressed sensing of images using directional transforms," in Proc. IEEE Int. Conf. on Image processing (ICIP), pp. 3021-3024, Nov. 2009.
  13. R. C. Gonzalez and R.E. Woods, Digital Image Processing, 2nd ed., Addison-Wesley, Reading, MA, 1992.
  14. Y. X. Yuan, "Step-sizes for the gradient method," in Proc. of the 3rd Int. Congress of Chinese Mathematicians, AMS/IP Studies in Advanced Mathematics, pp. 785-796, 2008.
  15. D. L. Donoho, "De-noising by soft thresholding," IEEE Trans. Info. Theory, vol. 41, no. 3, pp. 613-627, 1995. https://doi.org/10.1109/18.382009
  16. T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Appl. Computat. Harmon. Anal., vol. 27, no. 3, pp. 265-274, Nov. 2009. https://doi.org/10.1016/j.acha.2009.04.002
  17. The USC-SIPI image database. http://sipi.usc.edu/database/.

Cited by

  1. Rate Allocation for Block-based Compressive Sensing vol.20, pp.3, 2015, https://doi.org/10.5909/JBE.2015.20.3.398
  2. An Effective Fast Algorithm of BCS-SPL Decoding Mechanism for Smart Imaging Devices vol.19, pp.2, 2016, https://doi.org/10.9717/kmms.2016.19.2.200