Undersampled Hyperspectral Image Reconstruction Based on Surfacelet Transform

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