Super-resolution image reconstruction using fractional-order total variation and adaptive regularization parameters

Single-image super-resolution (SR) reconstruction aims to obtain a high-resolution (HR) image from a low-resolution (LR) image. In this paper, a hybrid single-image SR model integrated total variation (TV) and fractional-order TV (FOTV) is proposed to pursuit the adaptive reconstruction of the HR image. Specifically, fractional order in the proposed SR model is adaptively set according to the textural feature of the LR image firstly; then, the SR model is separated into two sub-models with each of them containing exactly one regularization parameter. These two sub-models are solved by using alternating direction multiplier method, and two regularization parameters are concurrently updated by using discrepancy principle. Finally, the solutions of two sub-models are interactively averaged to reconstruct HR image. The results of experiments indicated that the proposed hybrid SR model with adaptive regularization parameters has a comparative performance compared with state-of-the-art methods. Moreover, it would be potentially more adaptive for the condition of varied blurred kernels.

[1]  Wei Zhang,et al.  A Fast Adaptive Parameter Estimation for Total Variation Image Restoration , 2014, IEEE Transactions on Image Processing.

[2]  Wangmeng Zuo,et al.  Learning Deep CNN Denoiser Prior for Image Restoration , 2017, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[3]  Lei Zhang,et al.  Nonlocally Centralized Sparse Representation for Image Restoration , 2013, IEEE Transactions on Image Processing.

[4]  Lei Zhang,et al.  Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising , 2016, IEEE Transactions on Image Processing.

[5]  José M. Bioucas-Dias,et al.  Adaptive total variation image deblurring: A majorization-minimization approach , 2009, Signal Process..

[6]  Xiaoou Tang,et al.  Depth Map Super-Resolution by Deep Multi-Scale Guidance , 2016, ECCV.

[7]  Liang Xiao,et al.  Adaptive Fractional-order Multi-scale Method for Image Denoising , 2011, Journal of Mathematical Imaging and Vision.

[8]  Ke Chen,et al.  An automatic regularization parameter selection algorithm in the total variation model for image deblurring , 2013, Numerical Algorithms.

[9]  Stanley Osher,et al.  Image Super-Resolution by TV-Regularization and Bregman Iteration , 2008, J. Sci. Comput..

[10]  Jiashu Zhang,et al.  Fractional-order total variation combined with sparsifying transforms for compressive sensing sparse image reconstruction , 2016, J. Vis. Commun. Image Represent..

[11]  Raymond H. Chan,et al.  Parameter selection for total-variation-based image restoration using discrepancy principle , 2012, IEEE Transactions on Image Processing.

[12]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[13]  Michael Elad,et al.  On Single Image Scale-Up Using Sparse-Representations , 2010, Curves and Surfaces.

[14]  Liang Xiao,et al.  A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images , 2014, Signal Process..

[15]  Yi-Fei Pu,et al.  Fractional Differential Mask: A Fractional Differential-Based Approach for Multiscale Texture Enhancement , 2010, IEEE Transactions on Image Processing.

[16]  Brendt Wohlberg,et al.  UPRE method for total variation parameter selection , 2010, Signal Process..

[17]  Alain Oustaloup,et al.  Fractional differentiation for edge detection , 2003, Signal Process..

[18]  G. Vainikko.  The discrepancy principle for a class of regularization methods , 1982 .

[19]  Kyoung Mu Lee,et al.  Accurate Image Super-Resolution Using Very Deep Convolutional Networks , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[20]  Fang Li,et al.  Variational denoising of partly textured images , 2009, J. Vis. Commun. Image Represent..

[21]  Narendra Ahuja,et al.  Single image super-resolution from transformed self-exemplars , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

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

[23]  Rajeev Srivastava,et al.  Restoration of Poisson noise corrupted digital images with nonlinear PDE based filters along with the choice of regularization parameter estimation , 2013, Pattern Recognit. Lett..

[24]  Yang Wang,et al.  Joint Random Field Model for All-Weather Moving Vehicle Detection , 2010, IEEE Transactions on Image Processing.

[25]  Zhang Jun,et al.  A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising , 2011 .

[26]  Xavier Bresson,et al.  Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction , 2010, SIAM J. Imaging Sci..

[27]  Mudar Sarem,et al.  A novel multi-image super-resolution reconstruction method using anisotropic fractional order adaptive norm , 2014, The Visual Computer.

[28]  Aggelos K. Katsaggelos,et al.  Variational Bayesian Blind Deconvolution Using a Total Variation Prior , 2009, IEEE Transactions on Image Processing.

[29]  Xiaoou Tang,et al.  Learning a Deep Convolutional Network for Image Super-Resolution , 2014, ECCV.

[30]  Dianhui Wang,et al.  A fractional-order adaptive regularization primal-dual algorithm for image denoising , 2015, Inf. Sci..

[31]  Kyoung Mu Lee,et al.  Deeply-Recursive Convolutional Network for Image Super-Resolution , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

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

[33]  Junzhou Huang,et al.  Efficient MR Image Reconstruction for Compressed MR Imaging , 2010, MICCAI.

[34]  Stephen P. Boyd,et al.  An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems , 2012, 1203.1828.

[35]  Chuanjiang He,et al.  Fractional order total variation regularization for image super-resolution , 2013, Signal Process..

[36]  E. Maeland.  On the comparison of interpolation methods. , 1988, IEEE transactions on medical imaging.

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

[38]  E.T.F. Santos,et al.  L-and Y-curve approaches for the selection of regularization parameter in geophysical diffraction tomography , 2007 .

[39]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[40]  Wangmeng Zuo,et al.  Learning a Single Convolutional Super-Resolution Network for Multiple Degradations , 2017, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition.

[41]  Michael K. Ng,et al.  Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods , 2010, SIAM J. Sci. Comput..

[42]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[43]  Aline Roumy,et al.  Low-Complexity Single-Image Super-Resolution based on Nonnegative Neighbor Embedding , 2012, BMVC.