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Mathematical Problems in Engineering
Volume 2013, Article ID 470165, 11 pages
Research Article

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

1School of Computer Science & Engineering, Nanjing University of Science & Technology, Nanjing, Jiangsu 210094, China
2North Information Control Group Co. Ltd., Nanjing, Jiangsu 210094, China

Received 16 June 2013; Accepted 2 September 2013

Academic Editor: Suh-Yuh Yang

Copyright © 2013 Can Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).