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Journal of Zhejiang University SCIENCE C

, Volume 15, Issue 8, pp 664–674 | Cite as

Adaptive contourlet-wavelet iterative shrinkage/thresholding for remote sensing image restoration

  • Nu Wen
  • Shi-zhi Yang
  • Cheng-jie Zhu
  • Sheng-cheng Cui
Article
  • 107 Downloads

Abstract

In this paper, we present an adaptive two-step contourlet-wavelet iterative shrinkage/thresholding (TcwIST) algorithm for remote sensing image restoration. This algorithm can be used to deal with various linear inverse problems (LIPs), including image deconvolution and reconstruction. This algorithm is a new version of the famous two-step iterative shrinkage/thresholding (TwIST) algorithm. First, we use the split Bregman Rudin-Osher-Fatemi (ROF) model, based on a sparse dictionary, to decompose the image into cartoon and texture parts, which are represented by wavelet and contourlet, respectively. Second, we use an adaptive method to estimate the regularization parameter and the shrinkage threshold. Finally, we use a linear search method to find a step length and a fast method to accelerate convergence. Results show that our method can achieve a signal-to-noise ratio improvement (ISNR) for image restoration and high convergence speed.

Key words

Image restoration Adaptive Cartoon-texture decomposition Linear search Iterative shrinkage/thresholding 

CLC number

TP7 

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References

  1. Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T., 2010. Fast image recovery using variable splitting and constrained optimization. IEEE Trans. Image Process., 19(9):2345–2356. [doi:10.1109/TIP.2010.2047910]CrossRefMathSciNetGoogle Scholar
  2. Beck, A., Teboulle, M., 2009a. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems. IEEE Trans. Image Process., 18(11): 2419–2434. [doi:10.1109/TIP.2009.2028250]CrossRefMathSciNetGoogle Scholar
  3. Beck, A., Teboulle, M., 2009b. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci., 2(1):183–202. [doi:10.1137/080716542]CrossRefzbMATHMathSciNetGoogle Scholar
  4. Bioucas-Dias, J.M., 2006. Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors. IEEE Trans. Image Process., 15(4): 937–951. [doi:10.1109/TIP.2005.863972]CrossRefMathSciNetGoogle Scholar
  5. Bioucas-Dias, J.M., Figueiredo, M.A.T., 2007a. A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans. Image Process., 16(12): 2992–3004. [doi:10.1109/TIP.2007.909319]CrossRefMathSciNetGoogle Scholar
  6. Bioucas-Dias, J.M., Figueiredo, M.A.T., 2007b. Two-step algorithms for linear inverse problems with nonquadratic regularization. Proc. IEEE Int. Conf. on Image Processing, p.I-105–I-108. [doi:10.1109/ICIP.2007.4378902]Google Scholar
  7. Bioucas-Dias, J.M., Figueiredo, M.A.T., 2008. An iterative algorithm for linear inverse problems with compound regularizers. Proc. 15th IEEE Int. Conf. on Image Processing, p.685–688. [doi:10.1109/ICIP.2008.4711847]Google Scholar
  8. Bioucas-Dias, J.M., Figueiredo, M.A.T., Oliveira, J.P., 2006. Total variation-based image deconvolution: a majorization-minimization approach. Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, p.II. [doi:10.1109/ICASSP.2006.1660479]Google Scholar
  9. Buades, A., Le, T.M., Morel, J.M., et al., 2010. Fast cartoon+ texture image filters. IEEE Trans. Image Process., 19(8): 1978–1986. [doi:10.1109/TIP.2010.2046605]CrossRefMathSciNetGoogle Scholar
  10. Combettes, P.L., Wajs, V.R., 2005. Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul., 4(4):1168–1200. [doi:10.1137/050626090]CrossRefzbMATHMathSciNetGoogle Scholar
  11. Daubechies, I., Defrise, M., De Mol, C., 2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math., 57(11): 1413–1457. [doi:10.1002/cpa.20042]CrossRefzbMATHGoogle Scholar
  12. Figueiredo, M.A.T., Nowak, R.D., 2003. An EM algorithm for wavelet-based image restoration. IEEE Trans. Image Process., 12(8):906–916. [doi:10.1109/TIP.2003.814255]CrossRefzbMATHMathSciNetGoogle Scholar
  13. Figueiredo, M.A.T., Bioucas-Dias, J.M., Nowak, R.D., 2007. Majorization-minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process., 16(12): 2980–2991. [doi:10.1109/TIP.2007.909318]CrossRefMathSciNetGoogle Scholar
  14. Figueiredo, M.A.T., Bioucas-Dias, J.M., Afonso, M.V., 2009. Fast frame-based image deconvolution using variable splitting and constrained optimization. Proc. IEEE/SP 15th Workshop on Statistical Signal Processing, p.109–112. [doi:10.1109/SSP.2009.5278628]Google Scholar
  15. Gilles, J., Osher, S., 2011. Bregman Implementation of Meyer’s G-Norm for Cartoon+Textures Decomposition. UCLA CAM Report.Google Scholar
  16. Goldstein, T., Osher, S., 2009. The split Bregman method for L1-regularized problems. SIAM J. Imag. Sci., 2(2):323–343. [doi:10.1137/080725891]CrossRefzbMATHMathSciNetGoogle Scholar
  17. Hunter, D.R., Lange, K., 2004. A tutorial on MM algorithms. Am. Stat., 58(1):30–37. [doi:10.1198/0003130042836]CrossRefMathSciNetGoogle Scholar
  18. Meyer, Y., 2001. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: the Fifteenth Dean Jacqueline B. Lewis Memorial Lectures. American Mathematical Society Boston, MA, USA.Google Scholar
  19. Nesterov, Y., 1983. A method of solving a convex programming problem with convergence rate O(1/k2). Sov. Math. Doklady, 27(2):372–376.zbMATHGoogle Scholar
  20. Nowak, R.D., Figueiredo, M.A.T., 2001. Fast wavelet-based image deconvolution using the EM algorithm. Proc. 35th Asilomar Conf. on Signals, Systems and Computers, p.371–375. [doi:10.1109/ACSSC.2001.986953]Google Scholar
  21. Pan, H.J., Blu, T., 2011. Sparse image restoration using iterated linear expansion of thresholds. Proc. 18th IEEE Int. Conf. on Image Processing, p.1905–1908. [doi:10.1109/ICIP.2011.6115842]Google Scholar
  22. Pan, H.J., Blu, T., 2013. An iterative linear expansion of thresholds for l1-based image restoration. IEEE Trans. Image Process., 22(9):3715–3728. [doi:10.1109/TIP. 2013.2270109]CrossRefGoogle Scholar
  23. Rudin, L.I., Osher, S., Fatemi, E., 1992. Nonlinear total variation based noise removal algorithms. Phys. D, 60(1–4): 259–268. [doi:10.1016/0167-2789(92)90242-F]CrossRefzbMATHGoogle Scholar
  24. Wright, S.J., Nowak, R.D., Figueiredo, M.A.T., 2009. Sparse reconstruction by separable approximation. IEEE Trans. Signal Process., 57(7):2479–2493. [doi:10.1109/TSP.2009.2016892]CrossRefMathSciNetGoogle Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Nu Wen
    • 1
    • 2
    • 3
  • Shi-zhi Yang
    • 1
    • 2
  • Cheng-jie Zhu
    • 1
    • 2
    • 3
  • Sheng-cheng Cui
    • 1
    • 2
  1. 1.Anhui Institute of Optics and Fine MechanicsChinese Academy of SciencesHefeiChina
  2. 2.Key Laboratory of Optical Calibration and CharacterizationChinese Academy of SciencesHefeiChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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