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Journal of Sensors
Volume 2015, Article ID 256391, 11 pages
Research Article

Undersampled Hyperspectral Image Reconstruction Based on Surfacelet Transform

1Department of Mathematics, Shantou University, Shantou 515063, China
2Guangdong Provincial Key Laboratory of Digital Signal and Image Processing, Shantou University, Shantou 515063, China
3School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361005, China
4Department of Electronic Science, Xiamen University, Xiamen 361005, China

Received 7 July 2014; Revised 23 September 2014; Accepted 24 September 2014

Academic Editor: Yongqiang Zhao

Copyright © 2015 Lei Liu 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.


Hyperspectral imaging is a crucial technique for military and environmental monitoring. However, limited equipment hardware resources severely affect the transmission and storage of a huge amount of data for hyperspectral images. This limitation has the potentials to be solved by compressive sensing (CS), which allows reconstructing images from undersampled measurements with low error. Sparsity and incoherence are two essential requirements for CS. In this paper, we introduce surfacelet, a directional multiresolution transform for 3D data, to sparsify the hyperspectral images. Besides, a Gram-Schmidt orthogonalization is used in CS random encoding matrix, two-dimensional and three-dimensional orthogonal CS random encoding matrixes and a patch-based CS encoding scheme are designed. The proposed surfacelet-based hyperspectral images reconstruction problem is solved by a fast iterative shrinkage-thresholding algorithm. Experiments demonstrate that reconstruction of spectral lines and spatial images is significantly improved using the proposed method than using conventional three-dimensional wavelets, and growing randomness of encoding matrix can further improve the quality of hyperspectral data. Patch-based CS encoding strategy can be used to deal with large data because data in different patches can be independently sampled.