Abstract
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.
Highlights
Typical hyperspectral imaging (HSI) is acquired on satellites and aerospace probes and transmitted to grounds
Since this paper focuses on investigating the spatialspectral sparsity of HSI, a Gaussian random matrix is chosen as Φ because it is incoherent with the entire existing basis n1 x[n]
A patch-based Compressed sensing (CS) encoding scheme is designed to deal with large data
Summary
Typical hyperspectral imaging (HSI) is acquired on satellites and aerospace probes and transmitted to grounds. The huge amounts of data but scarce equipment hardware resources on satellites and aerospace severely limit the transmission and storage of hyperspectral images [1, 2]. Super-resolution reconstruction is used to improve the spatial resolution of HSI [3, 4] while compression can improve the transmission efficiency [5,6,7,8]. An optimal sparsifying transform is always important for sparse image reconstruction to reduce the reconstruction error. We introduce the surfacelet transform (ST) to sparsely represent hyperspectral images by making use of the spatial and spectral information.
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