This letter proposes a fast yet efficient method to solve the hyperspectral unmixing problem in the challenging unsupervised context, i.e., when the endmember spectral signatures are unknown. First, a coarse approximation of the hyperspectral image is computed by spatially averaging neighboring pixels, which significantly reduces the amount of pixels to be handled. This reduced set of hyperspectral pixels is unmixed to derive coarse solutions of the unmixing problem, i.e., coarse estimates of the endmember signatures and the corresponding low-resolution abundance maps. Then, the plain resolution abundance maps are estimated from the corresponding hyperspectral image based on the coarse endmember signatures. A sparsity promoting prior exploiting the low resolution map complements the conventional data fitting term to promote spatial smoothness while mitigating the loss of details in the edge areas. Finally, a least square optimization problem is solved to obtain the actual endmember signatures from the hyperspectral image and the abundance maps of plain resolution estimated in the previous step. Numerical experiments show that the proposed method is fast and performs well compared to state-of-the-art approaches from the literature.

We propose a simple yet efficient sparse unmixing method for hyperspectral images. It exploits the spatial and spectral properties of hyperspectral images by designing a new regularization informed by multiscale analysis. The proposed approach consists of two steps. First, a sparse unmixing is conducted on a coarse hyperspectral image resulting from a spatial smoothing of the original data. The estimated coarse abundance map is subsequently used to design two weighting terms summarizing the spatial and spectral properties of the image. They are combined to define a sparse regularization embedded into a unmixing problem associated with the original hyperspectral image at full resolution. The performance of the proposed method is assessed with numerous experiments conducted on synthetic and real datasets. It is shown to compete favorably with state-of-the-art methods from the literature with lower computational complexity.

An efficient spatial regularization method using superpixel segmentation and graph Laplacian regularization is proposed for the sparse hyperspectral unmixing method. Since it is likely to find spectrally similar pixels in a homogeneous region, we use a superpixel segmentation algorithm to extract the homogeneous regions by considering the image boundaries. We first extract the homogeneous regions, which are called superpixels, and then, a weighted graph in each superpixel is constructed by selecting$K$-nearest pixels in each superpixel. Each node in the graph represents the spectrum of a pixel, and edges connect the similar pixels inside the superpixel. The spatial similarity is investigated using the graph Laplacian regularization. Sparsity regularization for an abundance matrix is provided using a weighted sparsity promoting norm. Experimental results on simulated and real data sets show the superiority of the proposed algorithm over the well-known algorithms in the literature.

Sparse unmixing is an ill-posed inverse problem to find the abundances of each mineral in a scene using a large spectral library. Since the homogeneous regions tend to have similar fractional abundances, including spatial–contextual information increases the performance of an unmixing algorithm. In this letter, we propose a double spatial graph Laplacian regularization for sparse unmixing (DSGLSU). The proposed method consists of two steps. In the first step, hyperspectral data are approximated using a suitable transformation to generate scaled (coarse) data to exploit the interpixel information. Then, a sparsity constrained optimization problem is solved in the approximation domain to produce a coarse abundance matrix. A low-resolution abundance map is obtained by applying an inverse transformation to a coarse abundance map. In the second step, a graph Laplacian and weighted sparsity regularized optimization problem is solved in the original domain to obtain an abundance map where the low-resolution abundance map obtained in the first step is used as a weight term in sparsity regularization. We perform experiments on two simulated data sets and a real data set. It has been shown that the proposed method outperforms the state-of-the-art spatially regularized sparse unmixing methods proposed in the literature.

This paper proposes a weighted residual nonnegative matrix factorization (NMF) with spatial regularization to unmix hyperspectral data. NMF decomposes a matrix into the product of two nonnegative matrices. However, NMF is known to be generally sensitive to noise, which makes difficult to retrieve the global minimum of the underlying objective function. To overcome this limitation, we include a residual weighting mechanism in the conventional NMF formulation. This strategy treats each row of the residual based on the weighting factor. In this manner, residuals with large values are penalized less and residuals with small values are penalized more to make NMF based unmixing problem more robust. Furthermore, we include a weight term in the form of an ℓ1 norm regularizer to provide spatial information of the abundance matrix. Experimental results are conducted to validate the effectiveness of the proposed method.

This letter proposes a simple, fast yet efficient sparse hyperspectral unmixing algorithm. The proposed method consists of three main steps. First, a coarse approximation of the hyperspectral image is built using a off-the-shelf segmentation algorithm. Then, a low-resolution approximation of the abundance map is estimated by solving a weighted ℓ1-regularized problem on this coarse approximation of the hyperspectral data. Finally, this low-resolution abundance map is subsequently used to design a sparsity-promoting penalization which acts as a spatial regularization informed by the coarse abundance map. It is incorporated into another weighted ℓ1-regularized problem whose solution is a higher resolution abundance map. The computational efficiency of the two last steps is ensured by solving the two underlying optimization problems using an alternating direction method of multipliers. Extensive experiments conducted on simulated and real data show the effectiveness of the proposed method.

We propose a spatial-spectral hyperspectral image classification method based on multiscale superpixels and guided filter (MSS-GF). In order to use spatial information effectively, MSSs are used to get local information from different region scales. Sparse representation classifier is used to generate classification maps for each region scale. Then, multiple binary probability maps are obtained for each of the classification maps. Adding GF denoises the classification results and then improves the classification accuracy. Finally, the class label of each pixel is determined by majority voting rule.