Wavelet integrated residual dictionary training for single image super-resolution

Single image super-resolution (SISR) is an encouraging process for image processing applications, where the super-resolution (SR) problem is resolved by the sparse representation of a signal. This paper presents a novel single image SR algorithm based on sparse representation in the wavelet domain. Dictionary learning and sparse coding process for acquiring the high-frequency details into the wavelet domain, wavelet gives better results because wavelets promote the sparsity of the image and also provide structural information about the image. Our method combines the concept of residual image learning with the coupled K-SVD dictionary learning algorithm. Residual image is obtained by subtracting the level-one DWT approximation sub-band from level-two DWT approximation sub-band. The proposed method combined properties of wavelet decomposition such as preserving the high-frequency details, directionality-and compactness by learning the multiple dictionaries for each wavelet subband. Six wavelets integrated residual dictionaries are learned from level-one and level-two wavelet sub-band images, three for the low resolution and three for high-resolution wavelet subband images. By designing compact wavelet multiple dictionaries, we reduce the computational complexity as the number of dictionary atoms is small. The proposed algorithm is tested over four different datasets and compared with eight other super-resolution algorithms in terms of average Peak signal-to-noise ratio (PSNR) and Structural similarity index measure (SSIM). We also examine how super-resolved image can be affected by the dictionary size and patch size as these parameters play a very important role in reconstructing the HR images.