Reconstruction of RGB composite CT lung image by blind de-convolution for various blurring functions
Keywords:Image Restoration Degradation, Blur, Convolution, De-Convolution, CT.
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.
 R. Liu and J. Jia, â€œReducing boundary artifacts in image deconvolution,â€ in Proc. 15th IEEE Int. Conf. Image Process., Oct. 2008, pp. 505â€“508.
 Mariana S. C. Almeida and MÃ¡rio A. T. Figueiredo, â€œDeconvolving Images With Unknown Boundaries Using the Alternating Direction Method of Multipliers,â€ IEEE Transactions On Image Processing, Vol. 22, No. 8, August 2013. https://doi.org/10.1109/TIP.2013.2258354.
 T. Goldstein and S. Osher, â€œThe split Bregman method for l1-regularized problems,â€ SIAM J. Imag.Sci., vol. 2, pp. 323â€“343, 2009. https://doi.org/10.1137/080725891.
 M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, â€œAn Augmented Lagrangian Approach to Linear Inverse Problems with Compound Regularization,â€ in Proc. 17th IEEE Intern. Conf. Image Process.â€“ICIP, Sep. 2010, pp. 4169â€“4172. https://doi.org/10.1109/ICIP.2010.5650379.
 M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, â€œNon-cyclic Deconvolution Using an Augmented Lagrangian Method,â€ in Proc. IEEE Int. Conf. Comput. Tool (EUROCON), Apr. 2011, pp. 1â€“4. https://doi.org/10.1109/EUROCON.2011.5929360.
 M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, â€œAn Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems,â€ IEEE Trans. Image Process., vol. 20, no. 3, pp. 681â€“695, Mar. 2011. https://doi.org/10.1109/TIP.2010.2076294.
 M. Almeida and M. A. T. Figueiredo, â€œBlind Deblurring of Images with Unknown Boundaries Using the Alternating Direction Method of Multipliers,â€ 2013, to be published.
 A. Beck and M. Teboulle, â€œA Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems,â€ SIAM J. Imag.Sci., vol. 2, no. 1, pp. 183â€“202, 2009. https://doi.org/10.1137/080716542.
 S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, â€œDistributed Optimization And Statistical Learning Via The Alternating Direction Method of Multipliers,â€ Found. Trend Mach. Learn., vol. 3, no. 1, pp. 1â€“122, 2011. https://doi.org/10.1561/2200000016.
 J.-F. Cai, S. Osher, and Z. Shen, â€œSplit Bregman methods and frame based image restoration,â€ Multiscale Model. Simul., vol. 8, no. 2, pp. 337â€“369, 2009. https://doi.org/10.1137/090753504.
 P. L. Combettes and J.-C.Pesquet, â€œA Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery,â€ IEEE J. Sel. Topics Signal Process, vol.1, no. 4, pp. 564â€“574, Dec. 2007. https://doi.org/10.1109/JSTSP.2007.910264.
 M. Donatelli, C. Estatico, A. Martinelli, and S. Serra-Capizzano, â€œImproved Image Deblurring with Anti-Reflective Boundary Conditions and Re-Blurring,â€ Inverse Problems, vol. 22, no. 6, pp. 2035â€“2053, Oct. 2006. https://doi.org/10.1088/0266-5611/22/6/008.
 E. Esser, â€œApplications of Lagrangian Based Alternating Direction Methods and Connections to Split Bregman,â€ Dept. CAM, Univ. California, Los Angeles, CA, USA, Tech. Rep. 09-31, 2009.
 M. A. T. Figueiredo and J. M. Bioucas-Dias, â€œRestoration of poissonian images using alternating direction optimization,â€ IEEE Trans. Image Process., vol. 19, no. 12, pp.3133â€“3145, Dec. 2010. https://doi.org/10.1109/TIP.2010.2053941.
 M. Almeida and M. A. T. Figueiredo, â€œDeconvolving Images with Unknown Boundaries using the Alternating Direction Method of Multipliers,â€ IEEE Transactions on Image Processing, Vol. 22, No. 8, August 2013. https://doi.org/10.1109/TIP.2013.2258354.
 M. V. Afonso, J. M. Bioucas-Dias, and M. A. T. Figueiredo, â€œFast image recovery using variable splitting and constrained optimization,â€ IEEE Trans. Image Process., vol. 19, no. 9, pp. 2345â€“2356, Sep. 2010. https://doi.org/10.1109/TIP.2010.2047910.
 J. Bioucas-Dias and M. Figueiredo, â€œA new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,â€ IEEE Trans. Image Process., vol. 16, no. 12, pp. 2992â€“3004, Dec. 2007. https://doi.org/10.1109/TIP.2007.909319.
 T. F. Chan, A. M. Yip, F. E. Park, â€œSimultaneous Total Variation Image Inpainting Blind Deconvolution,â€ Int. J. Imag. Syst.Technol., vol.15, no.1, pp.92â€“102, Jul.2005. https://doi.org/10.1002/ima.20041.
 W. Deng and W. Yin, â€œOn the global and linear convergence of the generalized alternating direction method of multipliers,â€ Dept. Computational Appl. Math., Rice Univ., Houston, TX, USA, Tech. Rep. 12â€“14, 2012.
 M. Elad, P. Milanfar, and R. Rubinstein, â€œAnalysis versus synthesis in signal priors,â€ Inverse Problems, vol. 23, pp. 947â€“968, Apr. 2007. https://doi.org/10.1088/0266-5611/23/3/007.
 M. A. T. Figueiredo and R. Nowak, â€œAn EM algorithm for wavelet based image restoration,â€ IEEE Trans. Image Process., vol. 12, no. 8, pp. 906â€“916, Aug. 2003. https://doi.org/10.1109/TIP.2003.814255.
 P. L. Combettes and V. Wajs, â€œSignal recovery by proximal forward backward splitting,â€ SIAM J. Multiscale Model. Simul, vol. 4, no. 4, pp. 1168â€“1200, 2005. https://doi.org/10.1137/050626090.
 M. A. T. Figueiredo and J. M. Bioucas-Dias, â€œRestoration of Poisson Images Using Alternating Direction Optimization,â€ IEEE Trans. Image Process., vol. 19, no. 12, pp.3133â€“3145, Dec. 2010. https://doi.org/10.1109/TIP.2010.2053941.
 M. Tao and J. Yiang, â€œAlternating Direction Algorithms For Total Variation Deconvolution in Image Reconstruction,â€ Dept. Math., Nanjing Univ., China, Tech. Rep. TR0918, 2009.