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Fast Single Image Super-Resolution Using a New Analytical Solution for l2–l2 Problems

Ningning Zhao 1, 2 Qi Wei 1, 3 Adrian Basarab 2 Nicolas Dobigeon 1 Denis Kouamé 2 Jean-Yves Tourneret 1
1 IRIT-SC - Signal et Communications
IRIT - Institut de recherche en informatique de Toulouse
2 IRIT-TCI - Traitement et Compréhension d’Images
IRIT - Institut de recherche en informatique de Toulouse
Abstract : This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high- resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strate- gies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 –l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.
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Submitted on : Thursday, September 29, 2016 - 11:27:00 AM
Last modification on : Friday, January 29, 2021 - 2:06:18 PM
Long-term archiving on: : Friday, December 30, 2016 - 12:43:30 PM

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Ningning Zhao, Qi Wei, Adrian Basarab, Nicolas Dobigeon, Denis Kouamé, et al.. Fast Single Image Super-Resolution Using a New Analytical Solution for l2–l2 Problems. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2016, vol. 25 (n° 8), pp. 3683-3697. ⟨10.1109/TIP.2016.2567075⟩. ⟨hal-01373784⟩

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