Wavelet domain dictionary learning-based single image superresolution

Recently sparse representations over learned dictionaries have been proven to be a very successful representation method for many image processing applications. This paper proposes a new approach for increasing the resolution from a single low-resolution image. This approach is based on learned dictionaries in the wavelet domain. The proposed method combines many desired properties of wavelet-based representations such as compactness, directionality and analysis in many scales with the flexibility of redundant sparse representations. Such an approach serves for two main purposes. First, it sparsifies the training set, and second, it allows the design of structured dictionaries. Structured dictionaries better capture intrinsic image characteristics. Furthermore, the design of multiple structured dictionaries serves to reduce the number of dictionary atoms and consequently reduces the computational complexity. Three couples of wavelet subband dictionaries are designed using the K-SVD algorithm: three for the low-resolution and three for the high-resolution wavelet subband images. The image patch size and dictionary redundancy issues are empirically investigated in this work. Extensive tests indicate that a patch size of $$6\times 6$$6×6 and a dictionary width of 216 is a good compromise between computational complexity and representation quality. The proposed algorithm is shown to be superior to the leading spatial domain sparse representation techniques both visually and quantitatively with an average PSNR increase of 1.71 dB as tested over the Kodak data set. This result is also validated in terms of SSIM as a perceptual quality metric. It is shown that the proposed approach better restores the lost high-frequency details in the three wavelet detail subbands. Furthermore, the proposed algorithm is shown to significantly reduce the dictionary learning and sparse coding computational complexity.