Sparse representation based image deblurring and super resolution

In image restoration applications, Sparse representation which is a statistical image modelling technique has been widely used. The image restoration quality depends on sparse representation of the original image. Considering that the contents can vary across different images or different patches in a single image, so we have to study a number of sets of bases from a example image patches, one set of bases are selected to characterize the local sparse domain. For the sparse representation we introduce two regularization terms. First, to regularize the image local structures, a set of autoregressive models are considered. Second, the image non-local self-similarity is introduced as an additional regularization term. For better image restoration performance, the sparsity regularization parameter is estimated. The proposed method achieves much better results compared to Iterative Shrinkage/Thresholding in terms of convergence rate.