Split Bregmanized anisotropic total variation model for image deblurring

An anisotropic total variation based model is proposed for image deblurring.Split Bregman iteration is used to solve the proposed minimization problem.The recovered images has more textures and less stair-casing effect.The proposed method is robust to different degree of blur kernels.The proposed method is robust to different degree of Gaussian noise. In this paper, an effective image deblurring model is proposed to preserve sharp image edges by suppressing the stair-casing arising in the total variation (TV) based method by using the anisotropic total variation. To solve the difficult L1 norm problems, the split Bregman iteration is employed. Several synthetic degraded images are used for experiments. Comparison results are also made with total variation and nonlocal total variation based method. Experimental results show that the proposed method not only is robust to noise and different blur kernels, but also performs well on blurring images with more detailed textures, and the stair-casing effect is well suppressed.

[1]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Weiguo Gong,et al.  Total variation blind deconvolution employing split Bregman iteration , 2012, J. Vis. Commun. Image Represent..

[3]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[4]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[5]  Stanley Osher,et al.  Image Decomposition and Restoration Using Total Variation Minimization and the H1 , 2003, Multiscale Model. Simul..

[6]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[7]  Fadil Santosa,et al.  Recovery of Blocky Images from Noisy and Blurred Data , 1996, SIAM J. Appl. Math..

[8]  Aggelos K. Katsaggelos,et al.  Digital image restoration , 2012, IEEE Signal Process. Mag..

[9]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[10]  M. Grasmair,et al.  Anisotropic Total Variation Filtering , 2010 .

[11]  Raymond H. Chan,et al.  Inpainting by Flexible Haar-Wavelet Shrinkage , 2008, SIAM J. Imaging Sci..

[12]  J. Astola,et al.  A novel anisotropic local polynomial estimator based on directional multiscale optimizations , 2004 .

[13]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[14]  Wotao Yin,et al.  An Iterative Regularization Method for Total Variation-Based Image Restoration , 2005, Multiscale Model. Simul..

[15]  J. S. Moll The anisotropic total variation flow , 2005 .

[16]  Yin Zhang,et al.  A Fast Algorithm for Image Deblurring with Total Variation Regularization , 2007 .

[17]  Jaakko Astola,et al.  Anisotropic local likelihood approximations: theory, algorithms, applications , 2005, IS&T/SPIE Electronic Imaging.

[18]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[19]  T. Chan,et al.  Edge-preserving and scale-dependent properties of total variation regularization , 2003 .

[20]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

[21]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[22]  Stanley Osher,et al.  Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing , 2003, J. Sci. Comput..

[23]  W. Ring Structural Properties of Solutions to Total Variation Regularization Problems , 2000 .

[24]  Qianshun Chang,et al.  Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising , 2013, J. Appl. Math..

[25]  Jian-Feng Cai,et al.  Convergence of the linearized Bregman iteration for ℓ1-norm minimization , 2009, Math. Comput..

[26]  Gabriele Steidl,et al.  Restoration of images with rotated shapes , 2008, Numerical Algorithms.

[27]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[28]  Jérôme Darbon,et al.  SAR Image Regularization With Fast Approximate Discrete Minimization , 2009, IEEE Transactions on Image Processing.

[29]  S. Osher,et al.  Decomposition of images by the anisotropic Rudin‐Osher‐Fatemi model , 2004 .

[30]  Jian-Feng Cai,et al.  Split Bregman Methods and Frame Based Image Restoration , 2009, Multiscale Model. Simul..

[31]  Gjlles Aubert,et al.  Mathematical problems in image processing , 2001 .

[32]  Jian-Feng Cai,et al.  Linearized Bregman iterations for compressed sensing , 2009, Math. Comput..

[33]  Mila Nikolova,et al.  Local Strong Homogeneity of a Regularized Estimator , 2000, SIAM J. Appl. Math..

[34]  Adam M. Oberman,et al.  Anisotropic Total Variation Regularized L^1-Approximation and Denoising/Deblurring of 2D Bar Codes , 2010, 1007.1035.

[35]  Jian-Feng Cai,et al.  Framelet-Based Blind Motion Deblurring From a Single Image , 2012, IEEE Transactions on Image Processing.

[36]  Joachim Weickert,et al.  Anisotropic diffusion in image processing , 1996 .