Image Super Resolution via Adaptive \ell _{p} (0<p<1) Regularization and Sparse Representation
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 l0 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 lp0 p 1) 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 l adaptively, and we discuss an alternate iteration method for selecting p and l. We perform experiments, which demonstrates that the proposed lp(0 p 1) regularization nonconvex optimization method can outperform the convex optimization method and generate higher quality images.
IEEE Transactions on Neural Networks and Learning Systems