Spectral-Spatial Constrained Nonnegative Matrix Factorization for Spectral Mixture Analysis of Hyperspectral Images

Abstract

Hyperspectral Spectral Mixture Analysis (SMA), which intends to decompose mixed pixels into a collection of endmembers weighted by their corresponding fraction abundances, has been successfully used to tackle mixed-pixel problem in hyperspectral remote sensing applications. As an approach of decomposing a high-dimensional data matrix into the multiplication of two nonnegative matrices, Nonnegative Matrix Factorization (NMF) has shown its advantages and been widely applied to SMA. Unfortunately, most of the NMF-based unmixing methods can easily lead to an unsuitable solution, due to inadequate mining of spatial and spectral information and the influence of outliers and noise. To overcome such limitations, a spatial constraint over abundance and a spectral constraint over endmembers are imposed over NMF-based unmixing model for spectral-spatial constrained unmixing. Specifically, a spatial neighborhood preserving constraint is proposed to preserve the local geometric structure of the hyperspectral data by assuming that pixels in a spatial neighborhood generally fall into a low-dimensional manifold, while a minimum spectral distance constraint is formulated to optimize endmember spectra as compact as possible. Furthermore, to handle non-Gaussian noises or outliers, an L 2,1 -norm based loss function is ultimately adopted for the proposed Spectral-Spatial constrained Nonnegative Matrix Factorization (SS-NMF) model and a projected gradient (PG) based optimization algorithm is designed for optimization. Experimental results over both synthetic and realworld datasets demonstrate that the proposed spatial and spectral constraints can certainly improve the performance of NMF-based unmixing and outperform state-of-the-art NMF-based unmixing algorithms.Index Terms-Spectral mixture analysis (SMA), nonnegative matrix factorization (NMF), hyperspectral remote sensing, linear mixture model.

Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review

“…4) Other weight learning Different from the above perspectives to establish a graph regularizer, [113] was based on the local linear embedding assumption, where the weight matrix W is learned by minimizing the following equation:…”

“…Hence, the classical NMF model defined by the least-squares loss is sensitive to noise, leading to dramatically degrading the unmixing performance. To improve the robustness of NMF, many models have been reported based on certain metrics, including but not limited to bounded Itakura-Saito (IS) divergence [125], L 2,1 -norm regularizer [62], [113], [126], [127], CIM [90], [94], [128], [129], Cauchy function [130], and general robust loss function [131]. The bounded IS divergence was employed to address the additive, multiplicative, and mixed noises in HSIs [125].…”

“…Based on the L 1,2 -norm regularizer, He et al [126] used specific bands of the HSIs and modeled the sparse noise explicitly for significantly improving the robustness of NMF. The L 2,1 -norm was employed to replace Euclidean distance or KL divergence directly in [113], and the spectral-spatial constrained NMF (SS-NMF) model was developed to cope with non-Gaussian noises or outliers, whose reconstruction error is calculated by…”

Superpixel-Based Weighted Sparse Regression and Spectral Similarity Constrained for Hyperspectral Unmixing

“…For LSMM, the traditional unmixing approaches involve the content related to geometry [15], [16], [17], statistics [18], and matrix decomposition [19], [20], [21], [22], [23], [24], [25], [26]. The assumption of the existence of pure endmembers needs to be satisfied in the geometry-based unmixing method, but this is not always true.…”