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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 586014, 8 pages
Research Article

The Nonlocal Sparse Reconstruction Algorithm by Similarity Measurement with Shearlet Feature Vector

College of Information and Communication Engineering, Harbin Engineering University, Harbin, China

Received 24 August 2013; Revised 7 January 2014; Accepted 19 January 2014; Published 4 March 2014

Academic Editor: Yi-Hung Liu

Copyright © 2014 Wu Qidi 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.


Due to the limited accuracy of conventional methods with image restoration, the paper supplied a nonlocal sparsity reconstruction algorithm with similarity measurement. To improve the performance of restoration results, we proposed two schemes to dictionary learning and sparse coding, respectively. In the part of the dictionary learning, we measured the similarity between patches from degraded image by constructing the Shearlet feature vector. Besides, we classified the patches into different classes with similarity and trained the cluster dictionary for each class, by cascading which we could gain the universal dictionary. In the part of sparse coding, we proposed a novel optimal objective function with the coding residual item, which can suppress the residual between the estimate coding and true sparse coding. Additionally, we show the derivation of self-adaptive regularization parameter in optimization under the Bayesian framework, which can make the performance better. It can be indicated from the experimental results that by taking full advantage of similar local geometric structure feature existing in the nonlocal patches and the coding residual suppression, the proposed method shows advantage both on visual perception and PSNR compared to the conventional methods.