Coupled K-SVD dictionary learning algorithm in wavelet domain for single image super-resolution

In sparse-land model, Single Image Super Resolution (SISR) is achieved by highly vulnerable assumption that the sparse coefficients of low and high resolution image patch are similar. To overcome this weak assumption, a coupled K-Singular Value Decomposition (K-SVD) algorithm in wavelet domain is proposed. In proposed algorithm the best low-rank approximation given by SVD is implemented to simultaneously update the Low Resolution (LR) and High Resolution (HR) dictionaries by enforcing the equality of the sparse representation coefficients at two resolution levels. In this paper, we have exploited the directionality and scale persistence property of wavelet domain. Such properties ensure that coupling between signal features at two consecutive levels becomes more prominent. Three pairs of coupled low and high resolution wavelet sub-band dictionaries are designed. Given the low resolution image, sparse coefficients are approximated using the low resolution dictionary then high resolution image is reconstructed using the calculated sparse coefficients and high resolution dictionary. Compared to the state of the art algorithms, results are significantly improved in terms of PSNR and SSIM quality measures.

[1]  Michael Elad,et al.  Multi-Scale Dictionary Learning Using Wavelets , 2011, IEEE Journal of Selected Topics in Signal Processing.

[2]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[3]  Mahmoud Nazzal,et al.  Single image superresolution using sparsity and dictionary learning in wavelet domain , 2012, 2012 20th Signal Processing and Communications Applications Conference (SIU).

[4]  Mahmoud Nazzal,et al.  Wavelet domain dictionary learning-based single image superresolution , 2015, Signal Image Video Process..

[5]  Thomas S. Huang,et al.  Image Super-Resolution Via Sparse Representation , 2010, IEEE Transactions on Image Processing.

[6]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[7]  Thomas S. Huang,et al.  Coupled Dictionary Training for Image Super-Resolution , 2012, IEEE Transactions on Image Processing.

[8]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[9]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[10]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[11]  Michael Elad,et al.  Fast and robust multiframe super resolution , 2004, IEEE Transactions on Image Processing.

[12]  Michael Elad,et al.  A Plurality of Sparse Representations Is Better Than the Sparsest One Alone , 2009, IEEE Transactions on Information Theory.

[13]  Xiaogang Wang,et al.  Image Transformation Based on Learning Dictionaries across Image Spaces , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[14]  Christopher M. Bishop,et al.  Bayesian Image Super-Resolution , 2002, NIPS.

[15]  Pierre Vandergheynst,et al.  Fast orthogonal sparse approximation algorithms over local dictionaries , 2011, Signal Process..

[16]  Guillermo Sapiro,et al.  Supervised Dictionary Learning , 2008, NIPS.

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

[18]  Jian Xu,et al.  Coupled K-SVD dictionary training for super-resolution , 2014, 2014 IEEE International Conference on Image Processing (ICIP).