Piecewise linear regression-based single image super-resolution via Hadamard transform

Image super-resolution (SR) has extensive applications in surveillance systems, satellite imaging, medical imaging, and ultra-high definition display devices. The state-ofthe-art methods for SR still incur considerable running time. In this paper, we propose a novel approach based on Hadamard pattern and tree search structure in order to reduce the running time significantly. In this approach, LR (low-resolution)-HR (high-resolution) training patch pairs are classified into different classes based on the Hadamard patterns generated from the LR training patches. The mapping relationship between the LR space and the HR space for each class is then learned and used for SR. Experimental results show that the proposed method can achieve comparable accuracy as state-of-the-art methods with much faster running speed

Half hypersphere confinement for piecewise linear regression

Recent research in piecewise linear regression for Super-Resolution has shown the positive impact of training regressors with densely populated clusters whose datapoints are tight in the Euclidean space. In this paper we further research how to improve the locality condition during the training of regressors and how to better select them during testing time. We study the characteristics of the metrics best suited for the piecewise regression algorithms, in which comparisons are usually made between normalized vectors that lie on the unitary hypersphere. Even though Euclidean distance has been widely used for this purpose, it is suboptimal since it does not handle antipodal points (i.e. diametrically opposite points) properly, as vectors with same module and angle but opposite directions are, for linear regression purposes, identical. Therefore, we propose the usage of antipodally invariant metrics and introduce the Half Hypersphere Confinement (HHC), a fast alternative to Multidimensional Scaling (MDS) that allows to map antipodally invariant distances in the Euclidean space with very little approximation error By doing so, we enable the usage of fast search structures based on Euclidean distances without undermining their speed gains with complex distance transformations. The performance of our method, which we named HHC Regression (HHCR), applied to SuperResolution (SR) improves both in quality (PSNR) and it is faster than any other state-of-the-art method. Additionally, under an application-agnostic interpretation of our regression framework, we also test our algorithm for denoising and depth upscaling with promising results.Peer ReviewedPostprint (author's final draft

Half hypersphere confinement for piecewise linear regression

Recent research in piecewise linear regression for Super-Resolution has shown the positive impact of training regressors with densely populated clusters whose datapoints are tight in the Euclidean space. In this paper we further research how to improve the locality condition during the training of regressors and how to better select them during testing time. We study the characteristics of the metrics best suited for the piecewise regression algorithms, in which comparisons are usually made between normalized vectors that lie on the unitary hypersphere. Even though Euclidean distance has been widely used for this purpose, it is suboptimal since it does not handle antipodal points (i.e. diametrically opposite points) properly, as vectors with same module and angle but opposite directions are, for linear regression purposes, identical. Therefore, we propose the usage of antipodally invariant metrics and introduce the Half Hypersphere Confinement (HHC), a fast alternative to Multidimensional Scaling (MDS) that allows to map antipodally invariant distances in the Euclidean space with very little approximation error By doing so, we enable the usage of fast search structures based on Euclidean distances without undermining their speed gains with complex distance transformations. The performance of our method, which we named HHC Regression (HHCR), applied to SuperResolution (SR) improves both in quality (PSNR) and it is faster than any other state-of-the-art method. Additionally, under an application-agnostic interpretation of our regression framework, we also test our algorithm for denoising and depth upscaling with promising results.Peer Reviewe