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Combined First- and Second-Order Variational Model for Image Compressive Sensing

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  • Can Feng
  • Liang Xiao
  • Zhihui Wei

Abstract

A hybrid variational model combined first- and second-order total variation for image reconstruction from its finite number of noisy compressive samples is proposed in this paper. Inspired by majorization-minimization scheme, we develop an efficient algorithm to seek the optimal solution of the proposed model by successively minimizing a sequence of quadratic surrogate penalties. Both the nature and magnetic resonance (MR) images are used to compare its numerical performance with four state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm obtained a significant improvement over related state-of-the-art algorithms in terms of the reconstruction relative error (RE) and peak signal to noise ratio (PSNR).

Suggested Citation

  • Can Feng & Liang Xiao & Zhihui Wei, 2013. "Combined First- and Second-Order Variational Model for Image Compressive Sensing," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, October.
    • Handle: RePEc:hin:jnlmpe:470165
    DOI: 10.1155/2013/470165
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