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

Zhao, Ningning and Wei, Qi and Basarab, Adrian and Dobigeon, Nicolas and Kouamé, Denis and Tourneret, Jean-Yves Fast Single Image Super-Resolution Using a New Analytical Solution for l2–l2 Problems. (2016) IEEE Transactions on Image Processing, 25 (8). 3683-3697. ISSN 1057-7149

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Official URL: http://dx.doi.org/10.1109/TIP.2016.2567075


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.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF of the article can be found at IEEE Transactions on Image Processing website : http://ieeexplore.ieee.org/xpl/aboutJournal.jsp?punumber=83
HAL Id:hal-01373784
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > University of Cambridge (UNITED KINGDOM)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Chinese Scholarship Council - Thematic Trimester on Image Processing of the CIMI Labex
Deposited On:29 Sep 2016 09:26

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