Hyperspectral unmixing, which decomposes mixed pixels into endmembers and corresponding abundance maps of endmembers, has obtained much attention in recent decades. Most spectral unmixing algorithms based on non-negative matrix factorization (NMF) do not explore the intrinsic manifold structure of hyperspectral data space. Studies have proven image data is smooth along the intrinsic manifold structure. Thus, this paper explores the intrinsic manifold structure of hyperspectral data space and introduces manifold learning into NMF for spectral unmixing. Firstly, a novel projection equation is employed to model the intrinsic structure of hyperspectral image preserving spectral information and spatial information of hyperspectral image. Then, a graph regularizer which establishes a close link between hyperspectral image and abundance matrix is introduced in the proposed method to keep intrinsic structure invariant in spectral unmixing. In this way, decomposed abundance matrix is able to preserve the true abundance intrinsic structure, which leads to a more desired spectral unmixing performance. At last, the experimental results including the spectral angle distance and the root mean square error on synthetic and real hyperspectral data prove the superiority of the proposed method over the previous methods.

With a low spectral resolution hyperspectral sensor, the signal recorded from a given pixel against the complex background is a mixture of spectral contents. To improve the accuracy of classification and subpixel object detection, hyperspectral unmixing (HU) is under research in the field of remote sensing. Two factors affect the accuracy of unmixing results including the search of global rather than local optimum in the HU procedure and the spectral variability. With that in mind, this paper proposes a hierarchical weighted sparsity unmixing (HWSU) method to improve the separation of similar interclass endmembers. The hierarchical strategy with abundance sparsity representation in each layer aims to obtain the global optimal solution. In addition, considering the significance of different bands, a weighted matrix of spectra is used to decrease the variability of intra-class endmembers. Both simulations and experiments with real hyperspectral data show that the proposed method can correctly obtain distinct signatures, accurate abundance estimation, and outperforms previous methods. Additionally, the test data shows that the mean spectral angle distance is less than 0.12 and the root mean square error is superior to 0.01.

Due to the complex background and low spatial resolution of the hyperspectral sensor, observed ground reflectance is often mixed at the pixel level. Hyperspectral unmixing (HU) is a hot-issue in the remote sensing area because it can decompose the observed mixed pixel reflectance. Traditional sparse hyperspectral unmixing often leads to an ill-posed inverse problem, which can be circumvented by spatial regularization approaches. However, their adoption has come at the expense of a massive increase in computational cost. In this paper, a novel multiscale hierarchical model for a method of sparse hyperspectral unmixing is proposed. The paper decomposes HU into two domain problems, one is in an approximation scale representation based on resampling the method’s domain, and the other is in the original domain. The use of multiscale spatial resampling methods for HU leads to an effective strategy that deals with spectral variability and computational cost. Furthermore, the hierarchical strategy with abundant sparsity representation in each layer aims to obtain the global optimal solution. Both simulations and real hyperspectral data experiments show that the proposed method outperforms previous methods in endmember extraction and abundance fraction estimation, and promotes piecewise homogeneity in the estimated abundance without compromising sharp discontinuities among neighboring pixels. Additionally, compared with total variation regularization, the proposed method reduces the computational time effectively.