A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm

Single-image super-resolution reconstruction aims to obtain a high-resolution image from a low-resolution image. Since the super-resolution problem is ill-posed, it is common to use a regularization technique. However, the choice of the fidelity and regularization terms is not obvious, and it plays a major role in the quality of the desired high resolution image. In this paper, a hybrid single-image super-resolution model integrated with total variation (TV) and fractional-order TV is proposed to provide an effective reconstruction of the HR image. We develop an efficient numerical scheme for this model using the scalar auxiliary variable approach with an adaptive time stepping strategy. Thorough experimental results suggest that the proposed model and numerical scheme can reconstruct high quality results both quantitatively and perceptually.

[1]  Moon Gi Kang,et al.  Super-resolution image reconstruction: a technical overview , 2003, IEEE Signal Process. Mag..

[2]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

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

[4]  Paul Steinmann,et al.  Natural element analysis of the Cahn–Hilliard phase-field model , 2010 .

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

[6]  Jie Shen,et al.  A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows , 2017, SIAM Rev..

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

[8]  N. K. Bose,et al.  High resolution image formation from low resolution frames using Delaunay triangulation , 2002, IEEE Trans. Image Process..

[9]  Dacheng Tao,et al.  Single Image Superresolution via Directional Group Sparsity and Directional Features , 2015, IEEE Transactions on Image Processing.

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

[11]  José M. Bioucas-Dias,et al.  Hyperspectral compressive acquisition in the spatial domain via blind factorization , 2015, 2015 7th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS).

[12]  Ke Chen,et al.  A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution , 2015, SIAM J. Imaging Sci..

[13]  Michael Elad,et al.  Example-Based Regularization Deployed to Super-Resolution Reconstruction of a Single Image , 2009, Comput. J..

[14]  Liangpei Zhang,et al.  A locally adaptive L1-L2 norm for multi-frame super-resolution of images with mixed noise and outliers , 2014, Signal Process..

[15]  LiJie,et al.  Image super-resolution , 2016 .

[16]  Adrian Basarab,et al.  Alternating direction method of multipliers framework for super-resolution in ultrasound imaging , 2012, 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI).

[17]  Jie Li,et al.  Image super-resolution: The techniques, applications, and future , 2016, Signal Process..

[18]  S. Jitapunkul,et al.  A Robust Iterative Multiframe Super-Resolution Reconstruction using a Bayesian Approach with Lorentzian Norm , 2006, 2006 10th IEEE Singapore International Conference on Communication Systems.

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

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

[21]  R. Chan,et al.  An Adaptive Strategy for the Restoration of Textured Images using Fractional Order Regularization , 2013 .

[22]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[23]  Xavier Bresson,et al.  Nonlocal Mumford-Shah Regularizers for Color Image Restoration , 2011, IEEE Transactions on Image Processing.

[24]  Yücel Altunbasak,et al.  Super-resolution reconstruction of hyperspectral images , 2005 .

[25]  Brendt Wohlberg,et al.  Efficient Minimization Method for a Generalized Total Variation Functional , 2009, IEEE Transactions on Image Processing.

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

[27]  Xinbo Gao,et al.  Single-Image Super-Resolution Using Active-Sampling Gaussian Process Regression , 2016, IEEE Transactions on Image Processing.

[28]  Hsieh Hou,et al.  Cubic splines for image interpolation and digital filtering , 1978 .

[29]  Jie Shen,et al.  Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates , 2019, J. Comput. Phys..

[30]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[31]  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.

[32]  Mohamed-Jalal Fadili,et al.  Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients , 2008, Journal of Mathematical Imaging and Vision.

[33]  Jiang Yang,et al.  The scalar auxiliary variable (SAV) approach for gradient flows , 2018, J. Comput. Phys..

[34]  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).

[35]  Jean-Yves Tourneret,et al.  Fast Single Image Super-Resolution Using a New Analytical Solution for $\ell _{2}$ – $\ell _{2}$ Problems , 2016, IEEE Transactions on Image Processing.

[36]  Michal Irani,et al.  Super-resolution from a single image , 2009, 2009 IEEE 12th International Conference on Computer Vision.

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

[38]  Jian Bai,et al.  Fractional-Order Anisotropic Diffusion for Image Denoising , 2007, IEEE Transactions on Image Processing.

[39]  Zhiliang Zhu,et al.  Fast Single Image Super-Resolution via Self-Example Learning and Sparse Representation , 2014, IEEE Transactions on Multimedia.

[40]  Tony F. Chan,et al.  High-Order Total Variation-Based Image Restoration , 2000, SIAM J. Sci. Comput..

[41]  William T. Freeman,et al.  Example-Based Super-Resolution , 2002, IEEE Computer Graphics and Applications.

[42]  Edmund Y. Lam,et al.  Application of Tikhonov Regularization to Super-Resolution Reconstruction of Brain MRI Images , 2007, MIMI.

[43]  Lihua Yang,et al.  A robust multiframe super-resolution algorithm based on half-quadratic estimation with modified BTV regularization , 2013, Digit. Signal Process..

[44]  Arvid Lundervold,et al.  Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time , 2003, IEEE Trans. Image Process..

[45]  Pingkun Yan,et al.  Image Super-Resolution Via Double Sparsity Regularized Manifold Learning , 2013, IEEE Transactions on Circuits and Systems for Video Technology.

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