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The orthogonal-projection-based band selection (OPBS) algorithm is one of the newly proposed band selection methods. In this letter, we present a nonlinear version of the OPBS method, which is denoted as the Kernel-OPBS method. The OPBS method selects the desired bands one by one, and in each round of lookup, it chooses the band that has the maximum distance to the hyperplane spanned by the currently selected bands. Extending this algorithm to a feature space associated with the original input space through a certain nonlinear mapping function can provide a nonlinear version of the OPBS algorithm. Although it is basically intractable to compute the mapped bands due to the high dimensionality of the feature space produced by the nonlinear mapping function, the selection criterion of the Kernel-OPBS method is actually related to only the inner products of the mapped bands; thus, the kernel function can be applied and it is unnecessary to define the nonlinear mapping function. Experimental results on different data sets demonstrate that the selected bands obtained by the Kernel-OPBS method can achieve higher pixel classification performances than that by the OPBS method. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is a crucial technique for exploiting remotely sensed hyperspectral data, which aims to estimate a set of spectral signatures, called endmembers and their corresponding proportions, called abundances. Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to HU. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, the hyperspectral images (HSIs) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real applications. This paper proposes a novel spectral–spatial robust NMF model by incorporating $\ell _{2,1}$ norm and $\ell _{1,2}$ norm, which achieves robustness to band noise and pixel noise simultaneously. The Huber’s M-estimator is integrated into the proposed model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed spectral–spatial robust model are also efficiently learned and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance. [ABSTRACT FROM AUTHOR]

Band selection (BS) tries to find a few useful bands to represent the whole hyperspectral image cube. This letter proposes a novel unsupervised BS method based on the band correlation analysis (BCA). The BCA method tries to find a subset of bands that can well represent the whole image data set. To avoid the exhaustive search, the BCA method iteratively adds the band with the good representative ability and low redundancy into the selected band set, until the sufficient quantity of bands has been obtained. The redundancy and the representative ability of one band are computed by its correlation with the currently selected bands and the remaining unselected bands, respectively. Through constructing a correlation matrix of total bands, the BCA method can find the bands that with large amounts of information and low redundancy, which ensures that the selected bands are useful for the further applications like pixels classification. Experimental results on three different data sets demonstrate that the proposed method is very effective and can achieve the best performance among the competitors. [ABSTRACT FROM AUTHOR]

Band selection (BS) is a special case of the feature selection problem, and it tries to remove redundant bands and select a few informative and distinctive bands to represent the whole image cube. The maximum ellipsoid volume (MEV) method regards the band subset with the maximum volume as the optimal band combination. However, the MEV method cannot be directly applied for hyperspectral imagery due to the high dimensionality of the data sets. Therefore, we first combine MEV with the sequential forward search (SFS) and propose a new unsupervised BS method called MEV-SFS. Furthermore, a subtle relationship between the ellipsoid volume of the band set and the orthogonal projections (OPs) of the candidate bands is observed. Based on this relationship, we propose another equivalent method, namely, the OP-based BS (OPBS) method. OPBS is the fast version of MEV-SFS, and it has a better computational efficiency and the potential to determine the number of bands to be selected. We specifically explain the rationality of the MEV-based methods (MEV-SFS and OPBS) and illustrate their theoretical significance and physical meaning from different aspects. Theoretical analysis also demonstrates that OPBS can be regarded as a model or framework for BS, and thus, we further propose a third novel BS method named the OPBS-information divergence (OPBS-ID) method, which is a variant of OPBS. OPBS-ID can achieve a better classification performance than OPBS in many cases. Experimental results on different hyperspectral data sets demonstrate that the proposed methods have high computational efficiency, and the selected bands can achieve satisfactory classification performances. [ABSTRACT FROM AUTHOR]

Endmember extraction is an important and challenging step to solve the spectral unmixing problem. Most existing endmember extraction algorithms (EEAs) usually find image pixels as endmembers assuming the presence of pure pixels in an image scene or generate virtual endmembers without pure-pixel assumption. When some prevalent materials have pure-pixel representation and pure pixels of other less prevalent materials are absent in the image, it would be more appropriate to extract the endmembers of both prevalent and less prevalent materials, respectively. Therefore, a novel two-stage EEA is presented in this paper. In the first stage, conventional pure-pixel-based EEAs are applied to generate a candidate pixel set, and then spatial information of the candidate pixels is exploited to determine the endmembers of prevalent materials. In the second stage, given known endmembers of prevalent materials, a modified algorithm based on nonnegative matrix factorization is performed to generate the endmembers of less prevalent materials. The validity of the proposed algorithm is demonstrated by experiments based on synthetic mixtures and a real image scene. [ABSTRACT FROM AUTHOR]