We consider a variational model for single-image super-resolution based on the assumption that the image gradient of the target image is sparse. To promote jump sparsity, we use an isotropic and anisotropic \ell^{0 combined with a quadratic data fidelity, similarly as studied in [1] for general problems in signal recovery . For the numerical realisation of the model, we consider a converging ADMM algorithm. Differently from 1%DIFDELCMD < ]%%% , 2%DIFDELCMD < ]%%% , where approximate graph cuts and dynamic programming techniques were used for solving the non-convex substeps in the case of multivariate data, the proposed splitting allows to compute explicitly their solution by means of hard-thresholding and standard conjugate-gradient solvers. We compare quantitatively our results with several convex, nonconvex and deep-learning-based approaches for several synthetic and real-world data. Our numerical results show that combining super-resolution with gradient sparsity is particularly helpful for object detection and labelling tasks (such as QR scanning and land-cover classification), for which our results are shown to improve the classification precision of standard clustering algorithms and state-of-the art deep architectures 3 .
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 \ell^0 regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for general signal recovery problems . For the numerical realisation of the model, we %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that \ell^0 gradient-regularised super-resolved images can be effectively used to improve the accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches .
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image
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To promote jump sparsity, we use
We enforce this assumption by considering both
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anisotropic \ell^{0
an anisotropic \ell^0 regularisation on the image gradient
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problems in signal recovery
signal recovery problems
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consider a converging ADMM algorithm. Differently from
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1
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,
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2
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, where approximate graph cuts and dynamic programming techniques were used for solving the non-convex substeps in the case of multivariate data, the proposed splitting allows to compute explicitly their solution
propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently
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compare quantitatively
test our model on highly-degraded synthetic and real-world data and quantitatively compare
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convex, nonconvex and deep-learning-based approaches for several synthetic and real-world data. Our numerical results show that combining super-resolution with gradient sparsity is particularly helpful for object detection and labelling tasks (such as QR scanning and land-cover classification), for which our results are shown
variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that \ell^0 gradient-regularised super-resolved images can be effectively used
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classification precision of standard clustering algorithms and state-of-the art deep architectures
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3
accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches