Spectral Unmixing of Hyperspectral Imagery Using Multilayer NMF

Abstract

Abstract-Hyperspectral images contain mixed pixels due to low spatial resolution of hyperspectral sensors. Spectral unmixing problem refers to decomposing mixed pixels into a set of endmembers and abundance fractions. Due to nonnegativity constraint on abundance fractions, nonnegative matrix factorization (NMF) methods have been widely used for solving spectral unmixing problem. In this letter we proposed using multilayer NMF (MLNMF) for the purpose of hyperspectral unmixing. In this approach, spectral signature matrix can be modeled as a product of sparse matrices. In fact MLNMF decomposes the observation matrix iteratively in a number of layers. In each layer, we applied sparseness constraint on spectral signature matrix as well as on abundance fractions matrix. In this way signatures matrix can be sparsely decomposed despite the fact that it is not generally a sparse matrix. The proposed algorithm is applied on synthetic and real datasets. Synthetic data is generated based on endmembers from USGS spectral library. AVIRIS Cuprite dataset has been used as a real dataset for evaluation of proposed method. Results of experiments are quantified based on SAD and AAD measures. Results in comparison with previously proposed methods show that the multilayer approach can unmix data more effectively.Index Terms-Hyperspectral imaging, nonnegative matrix factorization (NMF), multilayer NMF (MLNMF), sparseness constraint, spectral unmixing.

A Probabilistic Weighted Archetypal Analysis Method with Earth Mover’s Distance for Endmember Extraction from Hyperspectral Imagery

“…To make a holistic comparison, five state-of-the-art endmember extraction methods including ICA [50], MLNMF [29], CONMF [51], RNMF [30] and AA [36] have been implemented and their endmember results are compared against that of PWAA-EMD. The extracted endmembers are evaluated with two popular measures, spectral angle distance (SAD) and root-mean-square-error (RMSE).…”

“…The matrix factorization methods formulate an optimization problem of blind source decomposition with many additive constraints (e.g., sparsity, low rank or positivity) to simultaneously estimate all the endmembers. Representative algorithms include sparse nonnegative matrix underapproximation (SNMU) [28], multilayer nonnegative matrix factorization (MLNMF) [29], robust nonnegative matrix factorization (RNMF) [30] and constrained nonnegative matrix factorization [12]. The statistical methods transform endmember extraction into a statistical inference problem and aim for the highly mixed hyperspectral image scenarios, with typical examples of independent component analysis (ICA) [31] and Bayesian algorithms such as normal endmember spectral unmixing [32] and the hierarchical Bayesian algorithm [33].…”

Kernel Multivariate Spectral–Spatial Analysis of Hyperspectral Data

“…In this paper, we have considered the most representative MVA approaches [4] such as principal component analysis (PCA) [2], canonical correlation analysis (CCA) [2], nonnegative matrix factorization [11], entropy component analysis, and also independent component analysis as dimensionality reduction methods. These MVA approaches include dimensionality reduction, feature extraction, and feature selection techniques and they are widely used in processing high-dimensional data.…”

Enhancing Hyperspectral Endmember Extraction Using Clustering and Oversegmentation-Based Preprocessing

“…They follow virtual endmembers with the underlying assumption that all mixed pixels are encompassed by a minimum volume simplex. Moreover, several hyperspectral unmixing techniques have been proposed by identifying endmembers and their designated abundance fractions simultaneously like nonnegative matrix factorization (NMF) [13], [14], multilayer NMF (MLNMF) [15], minimum volume enclosing simplex (MVES) [16], and graph-regularized NMF (GNMF) method combined with sparseness constraint [17]. All the aforementioned strategies consider hyperspectral data cube as a cloud irregularly involving huge spectral vectors without any spatial arrangements.…”