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ISRN Computational Mathematics
Volume 2012 (2012), Article ID 982792, 12 pages
http://dx.doi.org/10.5402/2012/982792
Research Article

Nonconvex Compressed Sampling of Natural Images and Applications to Compressed MR Imaging

1College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210046, China
2School of Mathematics and Statistics, Nanjing Audit University, Nanjing 211815, China
3School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China

Received 25 July 2011; Accepted 5 September 2011

Academic Editors: K. T. Miura and E. Weber

Copyright © 2012 Wenze Shao 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.

Abstract

There have been proposed several compressed imaging reconstruction algorithms for natural and MR images. In essence, however, most of them aim at the good reconstruction of edges in the images. In this paper, a nonconvex compressed sampling approach is proposed for structure-preserving image reconstruction, through imposing sparseness regularization on strong edges and also oscillating textures in images. The proposed approach can yield high-quality reconstruction as images are sampled at sampling ratios far below the Nyquist rate, due to the exploitation of a kind of approximate l0 seminorms. Numerous experiments are performed on the natural images and MR images. Compared with several existing algorithms, the proposed approach is more efficient and robust, not only yielding higher signal to noise ratios but also reconstructing images of better visual effects.