Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review
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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.Keywords:
Non-negative Matrix Factorization
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This study aims to extract the planted regions in partially forested area by analyzing the hyperspectral remote sensing images acquired with airborne platforms. The proposed study utilizes the endmember signatures obtained from hyperspectral unmixing algorithms in order to classify the image pixels. The classification algorithm selects the endmember with highest spectral vegetation characteristic, and associates this endmember with the planted area pixels. The algorithm is tested on a scene covering METU Ankara campus area that is acquired by high resolution hyperspectral push-broom sensor operating in visible and NIR range of the electromagnetic spectrum on October, 22 2014.
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Variable illumination and environmental, atmospheric, and temporal conditions cause the measured spectral signature for a material to vary within hyperspectral imagery. By ignoring these variations, errors are introduced and propagated throughout hyperspectral image analysis. To develop accurate spectral unmixing and endmember estimation methods, a number of approaches that account for spectral variability have been developed. This article motivates and provides a review for methods that account for spectral variability during hyperspectral unmixing and endmember estimation and a discussion on topics for future work in this area.
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Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing a hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, the hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared with methods analyzing the images independently. However, the significant size of the hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data. Finally, a comparison with independent unmixing algorithms illustrates the interest of the proposed strategy.
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This letter presents K-P-Means, a novel approach for hyperspectral endmember estimation. Spectral unmixing is formulated as a clustering problem, with the goal of K-P-Means to obtain a set of "purified" hyperspectral pixels to estimate endmembers. The K-P-Means algorithm alternates iteratively between two main steps (abundance estimation and endmember update) until convergence to yield final endmember estimates. Experiments using both simulated and real hyperspectral images show that the proposed K-P-Means method provides strong endmember and abundance estimation results compared with existing approaches.
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Hyperspectral unmixing (HU) refers to the process of decomposing the hyperspectral image into a set of endmember spectra and the corresponding set of abundance fractions. Non-negative matrix factorization (NMF) has been widely used in HU. However, most NMF-based unmixing methods have single-decomposition structures, which may have poor performance for highly mixed and ill-conditioned data. We proposed a sparsity-constrained multilayer NMF (MLNMF) method for spectral unmixing of highly mixed data. The MLNMF structure was established by decomposing the abundance matrix layer-by-layer to acquire the endmember matrix and the abundance matrix in the next layer. To reduce the space of solutions, sparsity constraints were added to the multilayer model by incorporating an L1 regularizer to the abundance matrix in each layer. Moreover, a layerwise strategy based on the Nesterov’s optimal gradient method was also proposed to optimize the multifactor NMF problem. Experiments on both synthetic data and real data demonstrate that our proposed method outperforms several other state-of-art approaches.
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Endmembers play an important role in many hyperspectral remote sensing applications, such as classification and Spectral Mixture Unmixing (SMU). In this paper, by considering endmembers as a small subset of pixels in a hyperspectral image, a sparse Linear Mixture Model (sLMM) is constructed to model the mixed pixels. As a result, an L 2,0 based sparse dictionary selection model is proposed for endmember extraction (EE) of hyperspectral images. Moreover, a Simultaneous Orthogonal Matching Pursuit (SOMP) based algorithm is adopted to extract endmembers efficiently. Experimental results on both synthetic and real hyperspectral data demonstrate our proposed EE algorithm outperforms several popular pure-pixel EE algorithms.
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A method of incorporating the multi-mixture pixel model into hyperspectral endmember extraction is presented and discussed. A vast majority of hyperspectral endmember extraction methods rely on the linear mixture model to describe pixel spectra resulting from mixtures of endmembers. Methods exist to unmix hyperspectral pixels using nonlinear models, but rely on severely limiting assumptions or estimations of the nonlinearity. This paper will present a hyperspectral pixel endmember extraction method that utilizes the bidirectional reflectance distribution function to model microscopic mixtures. Using this model, along with the linear mixture model to incorporate macroscopic mixtures, this method is able to accurately unmix hyperspectral images composed of both macroscopic and microscopic mixtures. The mixtures are estimated directly from the hyperspectral data without the need for a priori knowledge of the mixture types. Results are presented using synthetic datasets, of multi-mixture pixels, to demonstrate the increased accuracy in unmixing using this new physics-based method over linear methods. In addition, results are presented using a well-known laboratory dataset.
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Spectral mixture analysis is an important technique to analyze remotely sensed hyperspectral data sets. This approach involves the separation of a mixed pixel into its pure components or endmember spectra, and the estimation of the abundance value for each endmember. Several techniques have been developed for extraction of spectral endmembers and estimation of fractional abundances. However, an important issue that has not been yet fully accomplished is the incorporation of spatial constraints into endmember extraction and, particularly, fractional abundance estimation. Another relevant topic is the use of nonlinear versus linear mixture models, which can be unconstrained or constrained in nature. Here, the constraints refer to non-negativity and sum to unity of estimated fractional abundances for each pixel vector. In this paper, we investigate the impact of including spatial and abundance-related constraints in spectral mixture analysis of remotely sensed hyperspectral data sets. For this purpose, we discuss the advantages that can be obtained after including spatial information in techniques for endmember extraction and fractional abundance estimation, using a database of synthetic hyperspectral scenes with artificial spatial patterns generated using fractals, and a real hyperspectral scene collected by NASA's airborne visible infra-red imaging spectrometer (AVIRIS).
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Hyperspectral images are mixtures of spectra of materials in a scene. Accurate analysis of hyperspectral image requires spectral unmixing. The result of spectral unmixing is the material spectral signatures and their corresponding fractions. The materials are called endmembers. Endmember extraction equals to acquire spectral signatures of the materials. In this study, the authors propose a new hyperspectral endmember extraction algorithm for hyperspectral image based on QR factorisation using Givens rotations (EEGR). Evaluation of the algorithm is demonstrated by comparing its performance with two popular endmember extraction methods, which are vertex component analysis (VCA) and maximum volume by householder transformation (MVHT). Both simulated mixtures and real hyperspectral image are applied to the three algorithms, and the quantitative analysis of them is presented. EEGR exhibits better performance than VCA and MVHT. Moreover, EEGR algorithm is convenient to implement parallel computing for real‐time applications based on the hardware features of Givens rotations.
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