Abstract
This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.
Highlights
Due to the spatial resolution limitation of hyperspectral remote sensors as well as the diversity of surface features, mixed pixels are a common occurrence in hyperspectral images
To further alleviate the problems of the nonnegative matrix factorization (NMF)-based unsupervised nonlinear spectral unmixing (UNSU) methods, in this study, we propose two well-designed UNSU methods based on parameterized nonlinear least squares (PNLS) for the widely used generalized bilinear model (GBM) and Fan model
All the algorithms were initialized with the simplex growing algorithm (SGA) and fully constrained least squares (FCLS) and their combination SGA-FCLS was included in the experiment
Summary
Due to the spatial resolution limitation of hyperspectral remote sensors as well as the diversity of surface features, mixed pixels are a common occurrence in hyperspectral images. To alleviate the limitations of supervised nonlinear unmixing, the unsupervised nonlinear spectral unmixing (UNSU) provides a viable option and some attempts have been made to estimate simultaneously the endmembers and abundances (or nonlinearity coefficients) for nonlinear mixing models. To avoid the simple projection step which ensures nonnegativity, the unknown endmembers, abundances, and nonlinearity coefficients (only for the GBM) are parameterized by a Sigmoid function In this way, the LS/NLS problems with additional constraints are transformed into PNLS problems free of constraints. The proposed PNLS-based UNSU algorithms can obtain the endmembers, abundances, and nonlinearity coefficients (only for the GBM) simultaneously. The experimental results of synthetic and real data have verified that the proposed algorithms achieve better unmixing performance than the NMF-based UNSU algorithms for the GBM and the Fan model. The remainder of this paper is organized as follows: Section 2 provides a brief review of the GBM and Fan model; Section 3 details the proposed PNLS-based UNSU algorithms; Section 4 presents and analyses a series of experiments using both synthetic and real hyperspectral data; Section 5 concludes this paper
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