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access icon free Single-image super-resolution with total generalised variation and Shearlet regularisations

  • Author(s): Wensen Feng 1  and  Hong Lei 2
    • View affiliations
    • Affiliations: 1: School of Automation and Electrical Engineering, University of Science and Technology, Beijing 100083, People's Republic of China;
      2: Institute of Electronics, Chinese Academy of Science, Beijing 100190, People's Republic of China
  • Source: Volume 8, Issue 12, December 2014, p. 833 – 845
    DOI:  10.1049/iet-ipr.2013.0503 , Print ISSN 1751-9659, Online ISSN 1751-9667
© The Institution of Engineering and Technology
Received 14/07/2013, Accepted 28/02/2014, Revised 21/02/2014, Published 04/07/2014
Errata or comment

In this study, the authors proposed a novel regularisation model for resolution enhancement of clean or noisy single image based on the total generalised variation (TGV) and Shearlet transform. The proposed model has two main contributions. Firstly, different from models with total variation regularisation, which assume that images consist of piecewise-constant areas, the author's TGV-based model is aware of higher-order smoothness, thus eliminates the staircase-like artefacts. Secondly, various image features including edges and fine details can be preserved by their model. This is nature since the Shearlets mathematically provide an optimally sparse approximation for the class of piecewise-smooth functions with rich geometric information. Moreover, to solve the proposed model, an efficient numerical scheme is explicitly developed based on the Nesterov's algorithm. A series of numerical experiments validate the effectiveness of the proposed method.

Inspec keywords: approximation theory; image resolution; piecewise constant techniques; image enhancement; transforms

Other keywords: staircase-like artefacts; total variation regularisation; geometric information; Shearlet transform; total generalised variation; resolution enhancement; piecewise-smooth functions; clean single image; higher-order smoothness; optimally sparse approximation; TGV-based model; Shearlet regularisations; Nesterov algorithm; noisy single image; single-image super-resolution; piecewise-constant areas

Subjects: Integral transforms in numerical analysis; Optical, image and video signal processing; Interpolation and function approximation (numerical analysis); Computer vision and image processing techniques; Interpolation and function approximation (numerical analysis); Integral transforms in numerical analysis

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Erratum: ‘Single-image super-resolution with total generalised variation and Shearlet regularisations’
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