Constrained Nonnegative Tensor Factorization for Spectral Unmixing of Hyperspectral Images: A Case Study of Urban Impervious Surface Extraction

Abstract

In recent years, a new genre of hyperspectral unmixing methods based on nonnegative matrix factorization (NMF) have been proposed. Unlike traditional spectral unmixing methods, the NMF-based hyperspectral unmixing methods no longer depend on pure pixels in the original image. The NMF is based on linear algebra, which requires that the hyperspectral data cube is converted from 3-D cube to a 2-D matrix. Due to this conversion, the spatial information in the relative positions of the pixels is lost. With the emergence of multilinear algebra, the tensorial representation of hyperspectral imagery that preserves spectral and spatial information has become popular. The tensor-based spectral unmixing was first realized in 2017 using the matrix-vector nonnegative tensor factorization (MVNTF) decomposition. Using the construction of MVNTF spectral unmixing, this letter proposes to integrate three additional constraints (sparseness, volume, and nonlinearity) to the cost function. As we show in this letter, we found that the three constraints greatly improved the impervious surface area fraction/classification results. The constraints also shortened the processing time.