Reconstruction of RGB composite CT lung image by blind de-convolution for various blurring functions

  • Authors

    • Kalpana Vattikunta
    • Rajini G.K
    2018-02-09
    https://doi.org/10.14419/ijet.v7i1.8.9448
  • Image Restoration Degradation, Blur, Convolution, De-Convolution, CT.

  • Abstract

    A competent and flexible tool to optimize inverse problems related to image reconstruction by restoration is Alternating Direction Method of Multipliers (ADMM) with the knowledge of known blur. This method is later modified to perform Blind Image De-blurring (BID) of unknown blur on original image by using some function of regularization. But, in real world for de-blurring, the prior knowledge of blurring filter is important. In this research work, estimates of the image and blurring operator are obtained by considering significant image edges. An ADMM iteration criterion forms the base for which whiteness measurement parameter estimation which includes auto-correlation, auto-covariance. Using these parameters best ISNR is taken as input resulting from the iterations. Different degradation conditions are considered in the analysis to estimate the performance and to bring a conclusion to the degradation and restoration pair by processing composite and component images of the input RGB-CT lung image.

  • References

    1. [1] R. Liu and J. Jia, “Reducing boundary artifacts in image deconvolution,†in Proc. 15th IEEE Int. Conf. Image Process., Oct. 2008, pp. 505–508.

      [2] Mariana S. C. Almeida and Mário A. T. Figueiredo, “Deconvolving Images With Unknown Boundaries Using the Alternating Direction Method of Multipliers,†IEEE Transactions On Image Processing, Vol. 22, No. 8, August 2013. https://doi.org/10.1109/TIP.2013.2258354.

      [3] T. Goldstein and S. Osher, “The split Bregman method for l1-regularized problems,†SIAM J. Imag.Sci., vol. 2, pp. 323–343, 2009. https://doi.org/10.1137/080725891.

      [4] M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An Augmented Lagrangian Approach to Linear Inverse Problems with Compound Regularization,†in Proc. 17th IEEE Intern. Conf. Image Process.–ICIP, Sep. 2010, pp. 4169–4172. https://doi.org/10.1109/ICIP.2010.5650379.

      [5] M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Non-cyclic Deconvolution Using an Augmented Lagrangian Method,†in Proc. IEEE Int. Conf. Comput. Tool (EUROCON), Apr. 2011, pp. 1–4. https://doi.org/10.1109/EUROCON.2011.5929360.

      [6] M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems,†IEEE Trans. Image Process., vol. 20, no. 3, pp. 681–695, Mar. 2011. https://doi.org/10.1109/TIP.2010.2076294.

      [7] M. Almeida and M. A. T. Figueiredo, “Blind Deblurring of Images with Unknown Boundaries Using the Alternating Direction Method of Multipliers,†2013, to be published.

      [8] A. Beck and M. Teboulle, “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems,†SIAM J. Imag.Sci., vol. 2, no. 1, pp. 183–202, 2009. https://doi.org/10.1137/080716542.

      [9] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization And Statistical Learning Via The Alternating Direction Method of Multipliers,†Found. Trend Mach. Learn., vol. 3, no. 1, pp. 1–122, 2011. https://doi.org/10.1561/2200000016.

      [10] J.-F. Cai, S. Osher, and Z. Shen, “Split Bregman methods and frame based image restoration,†Multiscale Model. Simul., vol. 8, no. 2, pp. 337–369, 2009. https://doi.org/10.1137/090753504.

      [11] P. L. Combettes and J.-C.Pesquet, “A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery,†IEEE J. Sel. Topics Signal Process, vol.1, no. 4, pp. 564–574, Dec. 2007. https://doi.org/10.1109/JSTSP.2007.910264.

      [12] M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, “Improved Image Deblurring with Anti-Reflective Boundary Conditions and Re-Blurring,†Inverse Problems, vol. 22, no. 6, pp. 2035–2053, Oct. 2006. https://doi.org/10.1088/0266-5611/22/6/008.

      [13] E. Esser, “Applications of Lagrangian Based Alternating Direction Methods and Connections to Split Bregman,†Dept. CAM, Univ. California, Los Angeles, CA, USA, Tech. Rep. 09-31, 2009.

      [14] M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of poissonian images using alternating direction optimization,†IEEE Trans. Image Process., vol. 19, no. 12, pp.3133–3145, Dec. 2010. https://doi.org/10.1109/TIP.2010.2053941.

      [15] M. Almeida and M. A. T. Figueiredo, “Deconvolving Images with Unknown Boundaries using the Alternating Direction Method of Multipliers,†IEEE Transactions on Image Processing, Vol. 22, No. 8, August 2013. https://doi.org/10.1109/TIP.2013.2258354.

      [16] M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, “Fast image recovery using variable splitting and constrained optimization,†IEEE Trans. Image Process., vol. 19, no. 9, pp. 2345–2356, Sep. 2010. https://doi.org/10.1109/TIP.2010.2047910.

      [17] J. Bioucas-Dias and M. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,†IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992–3004, Dec. 2007. https://doi.org/10.1109/TIP.2007.909319.

      [18] T. F. Chan, A. M. Yip, F. E. Park, “Simultaneous Total Variation Image Inpainting Blind Deconvolution,†Int. J. Imag. Syst.Technol., vol.15, no.1, pp.92–102, Jul.2005. https://doi.org/10.1002/ima.20041.

      [19] W. Deng and W. Yin, “On the global and linear convergence of the generalized alternating direction method of multipliers,†Dept. Computational Appl. Math., Rice Univ., Houston, TX, USA, Tech. Rep. 12–14, 2012.

      [20] M. Elad, P. Milanfar, and R. Rubinstein, “Analysis versus synthesis in signal priors,†Inverse Problems, vol. 23, pp. 947–968, Apr. 2007. https://doi.org/10.1088/0266-5611/23/3/007.

      [21] M. A. T. Figueiredo and R. Nowak, “An EM algorithm for wavelet based image restoration,†IEEE Trans. Image Process., vol. 12, no. 8, pp. 906–916, Aug. 2003. https://doi.org/10.1109/TIP.2003.814255.

      [22] P. L. Combettes and V. Wajs, “Signal recovery by proximal forward backward splitting,†SIAM J. Multiscale Model. Simul, vol. 4, no. 4, pp. 1168–1200, 2005. https://doi.org/10.1137/050626090.

      [23] M. A. T. Figueiredo and J. M. Bioucas-Dias, “Restoration of Poisson Images Using Alternating Direction Optimization,†IEEE Trans. Image Process., vol. 19, no. 12, pp.3133–3145, Dec. 2010. https://doi.org/10.1109/TIP.2010.2053941.

      [24] M. Tao and J. Yiang, “Alternating Direction Algorithms For Total Variation Deconvolution in Image Reconstruction,†Dept. Math., Nanjing Univ., China, Tech. Rep. TR0918, 2009.

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  • How to Cite

    Vattikunta, K., & G.K, R. (2018). Reconstruction of RGB composite CT lung image by blind de-convolution for various blurring functions. International Journal of Engineering & Technology, 7(1.8), 40-45. https://doi.org/10.14419/ijet.v7i1.8.9448

    Received date: 2018-02-09

    Accepted date: 2018-02-09

    Published date: 2018-02-09