Efficient l0 Gradient-Based Super-Resolution for Simplified Image Segmentation

We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic l(0) regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMMsplitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugategradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several sparsity-promoting variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that thanks to the l(0) smoothing on the gradient, the super-resolved images can be used to improve the accuracy of standard segmentation algorithms for applications like QR codes and cell detection and land-cover classification problems. Index Terms-Single-image super-