Semi-Coupled Dictionary Learning for Single Image Super Resolution

It has been demonstrated in the literature that patches from natural images could be sparsely represented by using an over-complete dictionary of atoms. In fact sparse coding and dictionary learning (DL) have been shown to be very effective in image reconstruction. Some recent sparse coding methods with applications to super-resolution include supervised dictionary learning (SDL), online dictionary learning (ODL) and coupled dictionary learning (CDL). CDL method assumes that the coefficients of the representation of the two spaces are equal. However this assumption is too strong to address the flexibility of image structures in different styles. In this thesis a semi-coupled dictionary learning (SCDL) method has been simulated for the task of single image super-resolution (SISR). SCDL method assumes that there exists a dictionary pair over which the representations of two styles have a stable mapping and makes use of a mapping function to couple the coefficients of the low resolution and high resolution data. While tackling the energy minimization problem, SCDL will divide the main function into 3 sub-problems, namely (i) sparse coding for training samples, (ii) dictionary updating and (iii) mapping updating. Once a mapping function T and two dictionaries DH and DL are initialized, the sparse coefficients for the two sets of data can be obtained and afterwards the dictionary pairs can be updated. Finally, one can update the mapping function T through coding coefficients and dictionary. During the synthesis process, a patch based sparse recovery approach is used with selective sparse coding. Each patch at hand is first tested to belong to a certain cluster using the approximate scale invariance feature, then the dictionary pairs along with the mapping functions of that cluster are used for its reconstruction. First the low resolution patches of sparse coefficients are calculated by the selected dictionary which has low resolution, then, the patches of high resolution is obtained by using the dictionary which has high resolution and sparse coefficients of low resolution. In this thesis, comparisons between the proposed and the CDL algorithms of Yang and Xu were carried out using two image sets, namely: Set-A and Set-B. Set A had 14 test images and Set-B was composed of 10 test images, however in Set-B 8 of the test images were selected from text images which are in grayscale or in colour tone. Results obtained for Set-A show that based on mean PSNR values Yang’s method is the third best and Xu’s method is the second best. The sharpness measure based SCDL method was seen to be 0.03dB better than Xu’s method. For set-B only the best performing two methods were compared and it was seen that the proposed method had 0.1664dB edge over Xu’s method. The thesis also tried justifying the results, by looking at PSD of individual images and by calculating sharpness based scale invariance percentage for patches that classify under a number of clusters. It was noted that when most of the frequency components were around the low frequency region the proposed method would outperform Xu’s method in terms of PSNR. For images with a wide range of frequency components (spread PSD) when the number of HR patches in clusters C2 and/or C3 was low and their corresponding SM-invariance ratios were also low then the proposed method will not be as successful as Xu’s method. Keywords: sparse representations, super-resolution, semi-coupled dictionary learning, power spectral density, scale invariance.