Removing Boundary Artifacts for Real-Time Iterated Shrinkage Deconvolution

We propose a solution to the problem of boundary artifacts appearing in several recently published fast deblurring algorithms based on iterated shrinkage thresholding in a sparse domain and Fourier domain deconvolution. Our approach adapts an idea proposed by Reeves for deconvolution by the Wiener filter. The time of computation less than doubles.

[1]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[2]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

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

[4]  R. Nowak,et al.  Fast wavelet-based image deconvolution using the EM algorithm , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[5]  Michael K. Ng,et al.  Iterative Algorithms Based on Decoupling of Deblurring and Denoising for Image Restoration , 2008, SIAM J. Sci. Comput..

[6]  Benar Fux Svaiter,et al.  Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods , 2013, Math. Program..

[7]  Michael Elad,et al.  A wide-angle view at iterated shrinkage algorithms , 2007, SPIE Optical Engineering + Applications.

[8]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

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

[10]  Michael Elad,et al.  Analysis versus synthesis in signal priors , 2006, 2006 14th European Signal Processing Conference.

[11]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[12]  Javier Portilla,et al.  Image restoration through l0 analysis-based sparse optimization in tight frames , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[13]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[14]  Stanley J. Reeves,et al.  Fast image restoration without boundary artifacts , 2005, IEEE Transactions on Image Processing.

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

[16]  Tony F. Chan,et al.  A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science , 2010, SIAM J. Imaging Sci..

[17]  Michael Elad,et al.  Why Simple Shrinkage Is Still Relevant for Redundant Representations? , 2006, IEEE Transactions on Information Theory.

[18]  Filip Sroubek,et al.  Space-variant deblurring using one blurred and one underexposed image , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[19]  Nelly Pustelnik,et al.  Parallel Proximal Algorithm for Image Restoration Using Hybrid Regularization , 2009, IEEE Transactions on Image Processing.

[20]  D. Donoho,et al.  Redundant Multiscale Transforms and Their Application for Morphological Component Separation , 2004 .

[21]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[22]  Mário A. T. Figueiredo,et al.  Fast frame-based image deconvolution using variable splitting and constrained optimization , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[23]  Jian-Feng Cai,et al.  Linearized Bregman Iterations for Frame-Based Image Deblurring , 2009, SIAM J. Imaging Sci..

[24]  Stanley J. Reeves,et al.  Efficient Huber-Markov Edge-Preserving Image Restoration , 2006, IEEE Transactions on Image Processing.

[25]  Marc Teboulle,et al.  A proximal-based decomposition method for convex minimization problems , 1994, Math. Program..

[26]  N. Kingsbury Complex Wavelets for Shift Invariant Analysis and Filtering of Signals , 2001 .

[27]  José M. Bioucas-Dias,et al.  An iterative algorithm for linear inverse problems with compound regularizers , 2008, 2008 15th IEEE International Conference on Image Processing.

[28]  Fionn Murtagh,et al.  Fast communication , 2002 .