Fast minimization methods for solving constrained total-variation superresolution image reconstruction

In this paper, we study the problem of reconstructing a high-resolution image from several decimated, blurred and noisy low-resolution versions of the high-resolution image. The problem can be formulated as a combination of the total variation (TV) inpainting model and the superresolution image reconstruction model. The main purpose of this paper is to develop an inexact alternating direction method for solving such constrained TV image reconstruction problem. Experimental results are given to show that the proposed algorithm is effective and efficient.

[1]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[2]  M. Ng,et al.  Superresolution image reconstruction using fast inpainting algorithms , 2007 .

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

[4]  R. Rockafellar.  Monotone Operators and the Proximal Point Algorithm , 1976 .

[5]  Andy M. Yip,et al.  Simultaneous total variation image inpainting and blind deconvolution , 2005, Int. J. Imaging Syst. Technol..

[6]  Nirmal K. Bose,et al.  High‐resolution image reconstruction with multisensors , 1998, Int. J. Imaging Syst. Technol..

[7]  H. H. Rachford,et al.  On the numerical solution of heat conduction problems in two and three space variables , 1956 .

[8]  Michael K. Ng,et al.  A Fast Total Variation Minimization Method for Image Restoration , 2008, Multiscale Model. Simul..

[9]  Nirmal K. Bose,et al.  Mathematical analysis of super-resolution methodology , 2003, IEEE Signal Process. Mag..

[10]  R. Tyrrell Rockafellar,et al.  Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming , 1976, Math. Oper. Res..

[11]  Peyman Milanfar,et al.  A wavelet-based interpolation-restoration method for superresolution (wavelet superresolution) , 2000 .

[12]  S. Chaudhuri,et al.  Multi-objective super resolution: concepts and examples , 2003, IEEE Signal Process. Mag..

[13]  Dimitri P. Bertsekas,et al.  On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators , 1992, Math. Program..

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

[15]  Deepu Rajan,et al.  An MRF-Based Approach to Generation of Super-Resolution Images from Blurred Observations , 2004, Journal of Mathematical Imaging and Vision.

[16]  S. Chaudhuri.  Super-Resolution Imaging , 2001 .

[17]  M. Ng,et al.  Cosine transform preconditioners for high resolution image reconstruction , 2000 .

[18]  Bingsheng He,et al.  A new inexact alternating directions method for monotone variational inequalities , 2002, Math. Program..

[19]  Gilles Aubert,et al.  Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing , 2009, SIAM J. Sci. Comput..

[20]  D. Gabay.  Applications of the method of multipliers to variational inequalities , 1983 .

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

[22]  M. Nikolova.  A Variational Approach to Remove Outliers and Impulse Noise , 2004 .

[23]  M. Ng,et al.  Preconditioning regularized least squares problems arising from high-resolution image reconstruction from low-resolution frames , 2004 .

[24]  Michael K. Ng,et al.  A Fast Algorithm for Image Super-Resolution from Blurred Observations , 2006, EURASIP J. Adv. Signal Process..

[25]  Edmund Y. Lam,et al.  Superresolution imaging: Theory, Algorithms and Applications , 2007, Multidimens. Syst. Signal Process..

[26]  Peyman Milanfar,et al.  Super-Resolution Imaging: Analysis, Algorithms, and Applications , 2006, EURASIP J. Adv. Signal Process..

[27]  Michael K. Ng,et al.  Constrained total least‐squares computations for high‐resolution image reconstruction with multisensors , 2002, Int. J. Imaging Syst. Technol..

[28]  Gabriele Steidl,et al.  Removing Multiplicative Noise by Douglas-Rachford Splitting Methods , 2010, Journal of Mathematical Imaging and Vision.

[29]  Tony F. Chan,et al.  Mathematical Models for Local Nontexture Inpaintings , 2002, SIAM J. Appl. Math..

[30]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[31]  Michael K. Ng,et al.  A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors , 2001, Multidimens. Syst. Signal Process..

[32]  Michael K. Ng,et al.  Super-Resolution Image Restoration from Blurred Low-Resolution Images , 2005, Journal of Mathematical Imaging and Vision.

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

[34]  Fang Li,et al.  Selection of regularization parameter in total variation image restoration. , 2009, Journal of the Optical Society of America. A, Optics, image science, and vision.

[35]  R. Glowinski,et al.  Numerical Methods for Nonlinear Variational Problems , 1985 .

[36]  Bingsheng He,et al.  A unified framework of some proximal-based decomposition methods for monotone variational inequalities with separable structures , 2012 .