Fast total variation-based image restoration using blockwise accelerated proximal gradient approach

This paper proposes a blockwise accelerated proximal gradient (BAPG) approach. It chooses a block diagonal Lipschitz matrix in the generalized APG algorithm, such that the subproblems can be solved either by fast Fourier transform (FFT) or in closed forms. Experiments verify the great speed advantage of BAPG for total variation-based image restoration.

[1]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[2]  Junfeng Yang,et al.  A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration , 2009, SIAM J. Imaging Sci..

[3]  José M. Bioucas-Dias,et al.  An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems , 2009, IEEE Transactions on Image Processing.

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

[5]  Laurent D. Cohen,et al.  Non-local Regularization of Inverse Problems , 2008, ECCV.

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

[7]  Lei Zhang,et al.  Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization , 2010, IEEE Transactions on Image Processing.

[8]  José M. Bioucas-Dias,et al.  Restoration of Poissonian Images Using Alternating Direction Optimization , 2010, IEEE Transactions on Image Processing.

[9]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

[10]  Oleg V. Michailovich,et al.  An Iterative Shrinkage Approach to Total-Variation Image Restoration , 2009, IEEE Transactions on Image Processing.

[11]  Wotao Yin,et al.  Second-order Cone Programming Methods for Total Variation-Based Image Restoration , 2005, SIAM J. Sci. Comput..

[12]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[13]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[14]  K. Bredies,et al.  Linear Convergence of Iterative Soft-Thresholding , 2007, 0709.1598.

[15]  Arvind Ganesh,et al.  Fast algorithms for recovering a corrupted low-rank matrix , 2009, 2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).

[16]  Tony F. Chan,et al.  Total variation blind deconvolution , 1998, IEEE Trans. Image Process..

[17]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

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

[19]  Wangmeng Zuo,et al.  A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration , 2011, IEEE Transactions on Image Processing.

[20]  Shiqian Ma,et al.  An efficient algorithm for compressed MR imaging using total variation and wavelets , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  B. R. Hunt,et al.  Digital Image Restoration , 1977 .

[22]  Wotao Yin,et al.  Background correction for cDNA microarray images using the TV+L1 model , 2005, Bioinform..

[23]  José M. Bioucas-Dias,et al.  Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors , 2006, IEEE Transactions on Image Processing.

[24]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  J.-C. Pesquet,et al.  A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery , 2007, IEEE Journal of Selected Topics in Signal Processing.

[26]  Robert D. Nowak,et al.  An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..

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

[28]  Ernie Esser,et al.  Applications of Lagrangian-Based Alternating Direction Methods and Connections to Split Bregman , 2009 .

[29]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[30]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

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

[32]  Wotao Yin,et al.  Parametric Maximum Flow Algorithms for Fast Total Variation Minimization , 2009, SIAM J. Sci. Comput..

[33]  Simon Setzer,et al.  Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing , 2011, International Journal of Computer Vision.