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.