Abstract
Spectral unmixing is a consequential preprocessing task in hyperspectral image interpretation. With the help of large spectral libraries, unmixing is equivalent to finding the optimal subset of the library entries that can best model the image. Sparse regression techniques have been widely used to solve this optimization problem, since the number of materials present in a scene is usually small. However, the high mutual coherence of library signatures negatively affects the sparse unmixing performance. To cope with this challenge, a new algorithm called spectral-spatial low-rank sparse unmixing (SSLRSU) is established. In this article, the double weighting factors under the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> framework aim to improve the row sparsity of the abundance matrix and the sparsity of each abundance map. Meanwhile, the low-rank regularization term exploits the low-dimensional structure of the image, which makes for accurate endmember identification from the spectral library. The underlying optimization problem can be solved by the alternating direction method of multipliers efficiently. The experimental results, conducted by using both synthetic and real hyperspectral data, uncover that the proposed SSLRSU strategy can get accurate unmixing results over those given by other advanced sparse unmixing strategies.
Highlights
H YPERSPECTRAL imaging collects hundreds of images, using different wavelength channels, for the same area on the surface of the Earth [1]
Since each mixed pixel consists of only a few endmembers compared with the large spectral library, the abundance matrix usually contains a lot of zero values, that is, X is sparse
The regularization parameters of SUnSAL and double reweighted sparse unmixing (DRSU) were empirically set to λ = 0.001, λ = 0.0001, respectively, whereas the parameters for SUnSAL-total variation (TV), ADSpLRU, joint-sparse-blocks and low-rank unmixing (JSpBLRU), and spectral-spatial low-rank sparse unmixing (SSLRSU) were set to λ = 0.001, λT V = 0.001, and λ = 0.0005, τ = 0.001 and λ = 0.05, τ = 0.2 and λ = 0.003, τ = 0.2, respectively
Summary
H YPERSPECTRAL imaging collects hundreds of images, using different wavelength channels, for the same area on the surface of the Earth [1]. In order to better handle the high mutual coherence between spectral signatures in the library as well as consider the low-rank spatial structure of the abundance, a new spectral-spatial lowrank sparse unmixing (SSLRSU) is proposed. The low-rank constraint exploits the low-dimensional structure of the image and accurately identify endmember signatures from the spectral library. 1) For our new SSLRSU algorithm, the double weighting factors are utilized to upgrade the sparsity of the arrangement, while the low-rank constraint is used to preserve the spatial low-dimensional structure of abundance maps and improve the ability to identify endmembers from the spectral library. The spectral-spatial low-rank constraint effectively alleviates the negative impact of the high mutual coherence of the spectral library on the unmixing results.
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