With the help of endmember spectral library, sparse unmixing techniques have been successfully applied to hyperspectral image interpretation. The inclusion of spatial information in the sparse unmixing significantly improves the resulting fractional abundances. However, most existing spatial sparse unmixing algorithms are sensitive to noise and produce unstable solutions. To alleviate this drawback, a new robust double spatial regularization sparse unmixing (RDSRSU) method is proposed, which simultaneously exploits the spatial structure information from hyperspectral images and estimated abundance maps to mitigate the negative influence of noise on unmixing, so as to achieve robust sparse unmixing. To this end, a pre-calculated spatial weighting factor is introduced to maintain the original spatial information of the hyperspectral image. Meanwhile, the total variation spatial regularizer is used to capture the piecewise smooth structure of each abundance map. The experimental results, conducted by two sets of simulated data, as well as Cuprite and Mangrove real hyperspectral data, uncover that the proposed RDSRSU algorithm can offer better anti-noise ability and obtain more accurate results over those gave by other advanced sparse unmixing algorithms.

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 work, the double weighting factors under the ℓ1 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 gave by other advanced sparse unmixing strategies.

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