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

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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.

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References

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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]

    Article  MATH  MathSciNet  Google Scholar 

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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]

    Article  MATH  MathSciNet  Google Scholar 

  • 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]

    Article  MATH  Google Scholar 

  • 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]

    Article  MATH  MathSciNet  Google Scholar 

  • 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]

    Article  MathSciNet  Google Scholar 

  • 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 

  • Gilles, J., Osher, S., 2011. Bregman Implementation of Meyer’s G-Norm for Cartoon+Textures Decomposition. UCLA CAM Report.

    Google Scholar 

  • 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]

    Article  MATH  MathSciNet  Google Scholar 

  • Hunter, D.R., Lange, K., 2004. A tutorial on MM algorithms. Am. Stat., 58(1):30–37. [doi:10.1198/0003130042836]

    Article  MathSciNet  Google Scholar 

  • 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 

  • Nesterov, Y., 1983. A method of solving a convex programming problem with convergence rate O(1/k2). Sov. Math. Doklady, 27(2):372–376.

    MATH  Google Scholar 

  • 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 

  • 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 

  • 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]

    Article  Google Scholar 

  • 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]

    Article  MATH  Google Scholar 

  • 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]

    Article  MathSciNet  Google Scholar 

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Correspondence to Nu Wen.

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Project supported by the National Science & Technology Pillar Program (No. 2011BAB01B03), the National Natural Science Foun-dation of China (No. 41305019), and the Anhui Provincial Natural Science Foundation (No. 1308085QD70)

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Wen, N., Yang, Sz., Zhu, Cj. et al. Adaptive contourlet-wavelet iterative shrinkage/thresholding for remote sensing image restoration. J. Zhejiang Univ. - Sci. C 15, 664–674 (2014). https://doi.org/10.1631/jzus.C1300377

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  • DOI: https://doi.org/10.1631/jzus.C1300377

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