Multidimensional Systems and Signal Processing

, Volume 25, Issue 4, pp 683–701 | Cite as

Bayesian Shearlet shrinkage for SAR image de-noising via sparse representation

  • Shuai Qi Liu
  • Shao Hai Hu
  • Yang Xiao
  • Yong Li An


As SAR has been widely used nearly in every field, how to improve SAR’s image in both quality and visual effect has become necessary. Before what we really process the SAR image like image segmentation, edge detection, target detection or other processing, we must suppress the speckle noise in the image firstly. By analyzing the sorts and origins of noises, we present a new de-noising method of SAR image in the Shearlet domain based on sparse representation and Bayesian theory. Firstly, we apply the Shearlet transform to the noised SAR image. Secondly, we construct a new de-noising model via sparse representation and then use iterative algorithm based on Bayesian theory to solve it. Lastly, we can obtain the clean SAR image from the de-nosing Shearlet coefficients. The experimental results show that the proposed algorithm can not only effectively suppress speckle noise to improve the PSNR of SAR image, but also significantly improves the visual effect of SAR image, especially in enhancing the image’s texture.


SAR image de-nosing Sparse representation Shearlet de-nosing  Conjugate gradient method 



This project is supported by the National Natural Science Foundation of China: (No. 60572093), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050004016), Aviation Science Foundation (No. 201120M5007).


  1. Box, G. E. P., & Tiao, G. C. (1992). Bayesian inference in statistical analysis. Reading, MA: Addison Wesley.CrossRefMATHGoogle Scholar
  2. Candès, E. J., & Tao, T. (2006). Near-optimal signal recover from random projection: Universal encoding strategies? IEEE Transactions on Information Theory, 52(12), 5406–5425.CrossRefGoogle Scholar
  3. Chen, S., Donoho, D. L., & Saunders, M. A. (2001). Atomic decomposition by basis pursuit. SIAM Review, 43(1), 129–159.CrossRefMATHMathSciNetGoogle Scholar
  4. Chipman, H., Kolaczyk, E., & McCulloch, R. (1997). Adaptive bayesian wavelet shrinkage. Journal of the American Statistical Association, 92(440), 1413–1421.CrossRefMATHGoogle Scholar
  5. Dai, M., Peng, C., Chan, A. K., et al. (2004). Bayesian wavelet shrinkage with edge detection for SAR image despeckling. IEEE Transactions on Geoscience and Remote Sensing, 42(8), 1642–1648.CrossRefGoogle Scholar
  6. Do, M. N., & Vetterli, M. (2005). The contourlet transform: An efficient directional multiresolution image representation. IEEE Transactions on Image Processing, 14(12), 2091–2106.CrossRefMathSciNetGoogle Scholar
  7. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.CrossRefMATHMathSciNetGoogle Scholar
  8. Easley, G., Labate, D., & Lim, W. Q. (2008). Sparse directional image representation using the discrete shearlets transform. Applied and Computational Harmonic Analysis, 25(1), 25–46.CrossRefMATHMathSciNetGoogle Scholar
  9. Eom, K. B. (2011). Anisotropic adaptive filtering for speckle reduction in synthetic aperture radar images. Optical Engineering, 50(5), 97–108.CrossRefMathSciNetGoogle Scholar
  10. Fletcher, P. (1980). Practical methods of optimization, Unconstrained optimization. New York: Wiley, 1, 63–75.Google Scholar
  11. Frost, V. S., Stiles, J. A., Shanmugan, K. S., et al. (1982). Amode for radar image and its application to adaptive digital filtering of multiplicative noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4 (2), 157–165.Google Scholar
  12. Goodman, J. W. (1976). Some fundamental properties of speckle. Journal Optical Society America, 6(11), 1145–l150.CrossRefGoogle Scholar
  13. Guo, K., & Labate, D. (2007). Optimally sparse multidimensional representation using shearlets. SIAM Journal on Mathematical Analysis, 39(1), 298–318.CrossRefMATHMathSciNetGoogle Scholar
  14. Hou, B., Zhang, X. H., Bu, X. M., et al. (2012). SAR image despeckling based on nonsubsampled shearlet transform. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5(3), 809–823.CrossRefGoogle Scholar
  15. Lee, J. S., Jurkevich, L., Dewaeleb, P., et al. (1994). Speckle filtering of synthetic aperture radar images: A review. Remote Sensing Reviews, 8(4), 313–340.CrossRefGoogle Scholar
  16. Li, H. J., Zhang, J. S., & Chen, H. X. (2010). Image denoising based on the sparse land using redundant bandelet transform. Journal of the China Railway Society, 32(5), 108–113. (In Chinese).Google Scholar
  17. Lim, W. Q. (2010). The discrete shearlets transform: A new directional transform and compactly supported shearlets frames. IEEE Transactions Image Proccessing, 19(5), 1166–1180.CrossRefGoogle Scholar
  18. Milne, J. S. Algebraic number theory (v3.02). (2009). Available at
  19. Qin, H. L., Li, J., Zhou, H. X., et al. (2011). Infrared dim and small target background suppression using shearlet transform. Journal of Infrared and Millimeter Waves, 30(2), 162–166. (In Chinese).CrossRefGoogle Scholar
  20. Sheng, Y., Labate, D., Easley, G. R., et al. (2009). A shearlet approach to edge analysis and detection. IEEE Transactions on Image Processing, 18(5), 929–941.CrossRefMathSciNetGoogle Scholar
  21. Sun, Y. B., Wei, Z. H., Wu, M., et al. (2011). Image poisson denoising using sparse representations. Acta Electronica Sinica, 39(2), 285–290. (In Chinese).Google Scholar
  22. Tosic, I., Olshausen, B. A., & Culpepper, B. J. (2011). Learning sparse representations of depth. IEEE Journal of Selected Topics in Signal Processing, 5(5), 941–952.CrossRefGoogle Scholar
  23. Xiao, Q., Ding, X. H., Wang, S. J., Guo, D. H., et al. (2009). Image denoising based on adaptive over-complete sparse representation. Chinese Journal of Scientific Instrument, 30(9), 1886–1890. (In Chinese).Google Scholar
  24. Yu, C. P., Zhang, C. S., & Xie, L. H. (2012). A multiplicative Nakagami speckle reduction algorithm for ultrasound images. Multidimensional Systems and Signal Processing, 23(4), 499–513.CrossRefMathSciNetGoogle Scholar
  25. Zhao, R. Z., Liu, X. Y., Li, C. C., et al. (2009). Wavelet denoising via sparse representation. Science in China Series F, 52(8), 1371–1377.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Shuai Qi Liu
    • 1
  • Shao Hai Hu
    • 1
  • Yang Xiao
    • 1
  • Yong Li An
    • 2
  1. 1.Institute of Information ScienceBeijing Jiaotong UniversityBeijingPeople’s Republic of China
  2. 2.College of Information EngineeringHeBei United UniversityTangshanPeople’s Republic of China

Personalised recommendations