Hyperspectral linear unmixing based on collaborative sparsity and multi-band non-local total variation

In recent years, spectral unmixing is a hot issue in the hyperspectral remote sensing technology and applications. Within various methods, sparse regression is one of the most commonly used methods in the hyperspectral unmixing community. In order to overcome the limitation of spatial correlation of existing sparse unmixing methods and improve further the accuracy of sparsity representation, a novel hyperspectral linear unmixing method via fusion of collaborative sparsity and multi-band non-local total variation is proposed. This method analyses the sparsity and spatially geometrical structure of hyperspectral pixels by studying the linear spectral mixed model of hyperspectral images, and reveals the interior spatial correlation of hyperspectral images with the non-local variation framework. Specifically, the sparsity and spatial correlation of hyperspectral imagery are discussed, and a hyperspectral linear sparse unmixing model is afterwards constructed by combining the relaxation technique and non-local total variation framework. Second, the solution procedure of the above spectral unmixing model is divided into two steps under the variable separation method: fractional abundance estimation and abundance map restoration. The alternating direction method of multipliers (ADMM) and split Bregman operator are exploited to obtain the spectral unmixing results. Finally, the proposed hyperspectral unmixing algorithm is evaluated with synthetic and real hyperspectral datasets. In the experiments with a synthetic hyperspectral dataset, the feasibility and effectiveness of the method are analysed quantitatively and qualitatively. The quantitative metrics and visual examination of the estimated fractional abundance map are also better than the performance of the current mainstream hyperspectral sparse unmixing algorithms. Furthermore, two real hyperspectral datasets are applied to the algorithm of this work to prove its practicability.