Adaptive lq-norm constrained general nonlocal self-similarity regularizer based sparse representation for single image super-resolution

Abstract Sparse representation (SR) with the traditional nonlocal self-similarity (NLSS) regularizer has a brilliant future in handling single image super-resolution (SISR) inverse problem. However, such NLSS regularizers proposed so far always favor the fixed lq-norm constraint, making it difficult to cater the statistical diversity of the image content. As a result, the reconstruction capability of SR model is adversely influenced. To cope with the drawback, we first devise an adaptive lq-norm constrained general NLSS regularizer, which can integrate the advantages of the traditional NLSS prior and the row NLSS prior and adaptively assign different q values to handle the different image contents, and then incorporate it into SR model. Moreover, previous works only consider the additive white Gaussian noise case and neglect to research the impulse noise case in SR based SISR framework. For this purpose, our work will further consider these factors. Finally, both the iteratively reweighted least squares and the standard iterative shrinkage algorithms are adopted for solving our SR model. Experiments reveal that the reconstruction capability of our method is better than many outstanding SISR reconstruction methods.