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Mathematical Problems in Engineering
Volume 2014, Article ID 790547, 15 pages
Research Article

TV+TV2 Regularization with Nonconvex Sparseness-Inducing Penalty for Image Restoration

Key Laboratory of Data Analysis and Image Processing, Chongqing University of Arts and Sciences, Chongqing, China

Received 24 September 2013; Revised 2 January 2014; Accepted 16 January 2014; Published 4 March 2014

Academic Editor: Suh-Yuh Yang

Copyright © 2014 Chengwu Lu and Hua Huang. 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.


In order to restore the high quality image, we propose a compound regularization method which combines a new higher-order extension of total variation (TV+TV2) and a nonconvex sparseness-inducing penalty. Considering the presence of varying directional features in images, we employ the shearlet transform to preserve the abundant geometrical information of the image. The nonconvex sparseness-inducing penalty approach increases robustness to noise and image nonsparsity. In what follows, we present the numerical solution of the proposed model by employing the split Bregman iteration and a novel p-shrinkage operator. And finally, we perform numerical experiments for image denoising, image deblurring, and image reconstructing from incomplete spectral samples. The experimental results demonstrate the efficiency of the proposed restoration method for preserving the structure details and the sharp edges of image.