Super Resolution by Comprehensively Exploiting Dependencies of Wavelet Coefficients

We propose an algorithm for single image super resolution (SR) using wavelet decomposition and machine learning. Wavelets have been used for SR before due to their ability to capture scale invariant properties of natural images. However previous techniques used only a subset of relationships that exist between multiscale wavelet coefficients. We present a first-of-its-kind analysis of the wavelet properties relevant to SR that leads to insights for a novel SR algorithm. In particular we discovered that to estimate a desired finer scale detail coefficient it is not enough to use only its parent detail coefficient at the coarser scale as was done by the previous techniques. The estimation can be improved a lot by using certain additional coarser level detail coefficients and even finer scale approximation coefficients whose relative locations are suggested by our analysis. Additionally the previous wavelet-based techniques used generative learning frameworks for SR. However we show that SR is a type of problem on which discriminative frameworks excel. These improvements allowed our technique to far surpass the reconstruction accuracy of the previous wavelet-based SR algorithms on a large set of images. Additionally our algorithm also surpassed other state-of-the-art SR algorithms that are not based on wavelets in reconstruction quality and training and testing speeds. We thus reestablish the utility of the wavelets for SR.