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Previous studies have shown that image patches can be well represented as a sparse linear combination of elements from an appropriately selected over-complete dictionary. Recently, single-image super-resolution (SISR) via sparse representation using blurred and downsampled low-resolution images has attracted increasing interest, where the aim is to obtain the coefficients for sparse representation by solving an l0 or l1 norm optimization problem. The l0 optimization is a nonconvex and NP-hard problem, while the l1 optimization usually requires many more measurements and presents new challenges even when the image is the usual size, so we propose a new approach for SISR recovery based on regularization nonconvex optimization. The proposed approach is potentially a powerful method for recovering SISR via sparse representations, and it can yield a sparser solution than the l1 regularization method. We also consider the best choice for lp regularization with all p in (0, 1), where we propose a scheme that adaptively selects the norm value for each image patch. In addition, we provide a method for estimating the best value of the regularization parameter λ adaptively, and we discuss an alternate iteration method for selecting p and λ . We perform experiments, which demonstrates that the proposed regularization nonconvex optimization method can outperform the convex optimization method and generate higher quality images.
Cao et al. (Wed,) studied this question.