Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role in solving this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the article with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.
In the above article [1] , it should be noted that the second value of each column in the last row of Table I (i.e., 0.52%, 0.35%, 0.51%, and 0.72%) is calculated using average deviation rather than standard deviation. In order to be consistent with the title of Table I in [1] , the corresponding standard deviations are provided here.
Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role to solve this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the paper with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.
Hyperspectral unmixing is concerned with how to learn the constituent materials (called endmembers) and their corresponding proportions (called abundances) from mixed pixels. Nonnegative tensor factorization (NTF) is powerful in addressing the unmixing problem owing to the ability to preserve spatial inherent information. However, the neglect of local spatial information, nonlinear mixtures, and spectral variability degrades the quality of unmixing result. In this article, we propose a superpixel-based low-rank tensor factorization (SLRTF) for blind nonlinear hyperspectral unmixing. Our method first generates numerous superpixels and processes them into regular cubes to exploit the local spatial information. Then, the resulting superpixel cubes are jointly decomposed using a nonlinear low-rank tensor factorization based on a generalized bilinear model (GBM) to account for the second-order scattering phenomenon. Notably, each superpixel cube yields an endmember matrix to consider spectral variability. Furthermore, to make full use of the consistent and complementary spectral information, a double-weighted endmember (DWE) constraint is designed for adaptively learning the consensus endmember matrix. The tensor nuclear norm constraint is enforced on the abundance tensor to characterize high spatial correlation. Finally, the proposed method is compared with several state-of-the-art methods on synthetic and real datasets. Experimental results demonstrate that the proposed method offers superior performance for hyperspectral unmixing.
In order to unmix the hyperspectral imagery (HSI) with better performance, this letter proposes a correntropy-based autoencoder-like nonnegative matrix factorization (NMF) (CANMF) with total variation (CANMF-TV) method. NMF is extensively applied to unmix the mixed pixels. However, it only reconstructs the original data from the abundances in endmember space. To directly project the original data space into the endmember space, and then achieve the abundance matrix, we first exploit an autoencoder-like NMF for hyperspectral unmixing, which integrates both decoder and encoder . Considering that HSI is typically degraded by noise, the correntropy-induced metric (CIM) is introduced to construct a CANMF model. In addition, TV regularizer is imposed into the CANMF model so as to preserve the spatial-contextual information by promoting the piecewise smoothness of abundances. Finally, a series of experiments are conducted on both synthetic and real data sets, demonstrating the effectiveness of the proposed CANMF-TV method over comparison.
Hyperspectral unmixing refers to a source separation problem of decomposing a hyperspectral imagery (HSI) to estimate endmembers, and their corresponding abundances. Recently, matrix-vector nonnegative tensor factorization (MV-NTF) was proposed for unmixing to avoid structure information loss, which is caused by the HSI cube unfolding in nonnegative matrix factorization (NMF)-based methods. However, MV-NTF ignores local spatial information due to directly dealing with data as a whole, meanwhile, the forceful rank constraint in low-rank tensor decomposition loses some detailed structures. Unlike MV-NTF works at the original data, the pixel-based NMF is more adaptive to learn local spatial variations. Hence, from the perspective of multi-view, itis significant to utilize the complementary advantages of MV-NTF and NMF to fully preserve the intrinsic structure information, and exploit more detailed spatial information. In this article, we propose a sparsity-constrained coupled nonnegative matrix-tensor factorization (SCNMTF) model for unmixing, wherein MV-NTF and NMF are subtly coupled by sharing endmembers and abundances. Since the representations for abundances in MV-NTF and NMF are distinct, abundance sharing is achieved indirectly by introducing an auxiliary constraint. Furthermore, the L 1/2 regularizer is adopted to promote the sparsity of abundances. A series of experiments on synthetic and real hyperspectral data demonstrate the effectiveness of the proposed SCNMTF method.
Hyperspectral unmixing is a critical processing step for many remote sensing applications. Nonnegative matrix factorization (NMF) has drawn extensive attention in hyperspectral image analysis recently. Considering that the abundance matrix is generally sparse and smooth, we propose a sparsity-constrained NMF with adaptive total variation (SNMF-ATV) algorithm for hyperspectral unmixing. Specifically, the ATV could promote the smoothness of the estimated abundances while avoid the staircase effect caused by TV model. The comparison with other unmixing methods on both synthetic and real data sets demonstrates the effectiveness and superiority of the proposed SNMF-ATV algorithm with regard to the other considered methods.
Hyperspectral unmixing is an important processing step for many hyperspectral applications, mainly including: 1) estimation of pure spectral signatures (endmembers) and 2) estimation of the abundance of each endmember in each pixel of the image. In recent years, nonnegative matrix factorization (NMF) has been highly attractive for this purpose due to the nonnegativity constraint that is often imposed in the abundance estimation step. However, most of the existing NMF-based methods only consider the information in a single layer while neglecting the hierarchical features with hidden information. To alleviate such limitation, in this paper, we propose a new sparsity-constrained deep NMF with total variation (SDNMF-TV) technique for hyperspectral unmixing. First, by adopting the concept of deep learning, the NMF algorithm is extended to deep NMF model. The proposed model consists of pretraining stage and fine-tuning stage , where the former pretrains all factors layer by layer and the latter is used to reduce the total reconstruction error. Second, in order to exploit adequately the spectral and spatial information included in the original hyperspectral image, we enforce two constraints on the abundance matrix. Specifically, the $L_{1/2}$ constraint is adopted, since the distribution of each endmember is sparse in the 2-D space. The TV regularizer is further introduced to promote piecewise smoothness in abundance maps. For the optimization of the proposed model, multiplicative update rules are derived using the gradient descent method. The effectiveness and superiority of the SDNMF-TV algorithm are demonstrated by comparing with other unmixing methods on both synthetic and real data sets.
Hyperspectral unmixing is a critical step to process hyperspectral images (HSIs). Nonnegative matrix factorization (NMF) has drawn extensive attention in remotely sensed hyperspectral unmixing since it does not require prior knowledge about the pure spectral constituents (endmembers) in the scene. However, this approach is normally implemented as a single-layer procedure, which does not allow for a refinement of the obtained endmember abundances. In addition, HSIs suffer from the interference of sparse noise (besides Gaussian noise), which brings challenges when pursuing efficient hyperspectral unmixing. To address these issues, we propose a new self-supervised robust deep matrix factorization (SSRDMF) model for hyperspectral unmixing, which consists of two parts: encoder and decoder . In the encoder , a multilayer nonlinear structure is designed to directly map the observed HSI data to the corresponding abundances. The abundances are then decoded by the decoder , in which the connected weights are treated as the extracted endmembers. By modeling the sparse noise explicitly, the proposed method can reduce the effect caused by both Gaussian and sparse noise. Furthermore, a self-supervised constraint is included for exploring the spectral information, which is beneficial to further improve unmixing performance. To validate our method, we have conducted extensive experiments on both synthetic and real datasets. Our experiments reveal that our newly developed SSRDMF achieves superior unmixing performance compared to other state-of-the-art methods.
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