Blind Hyperspectral Unmixing Based on Graph Total Variation Regularization

Abstract

Remote sensing data from hyperspectral cameras suffer from limited spatial resolution, in which a single pixel of a hyperspectral image may contain information from several materials in the field of view. Blind hyperspectral image unmixing is the process of identifying the pure spectra of individual materials (i.e., endmembers) and their proportions (i.e., abundances) at each pixel. In this paper, we propose a novel blind hyperspectral unmixing model based on the graph total variation (gTV) regularization, which can be solved efficiently by the alternating direction method of multipliers (ADMM). To further alleviate the computational cost, we apply the Nyström method to approximate a fully-connected graph by a small subset of sampled points. Furthermore, we adopt the Merriman-Bence-Osher (MBO) scheme to solve the gTV-involved subproblem in ADMM by decomposing a grayscale image into a bit-wise form. A variety of numerical experiments on synthetic and real hyperspectral images are conducted, showcasing the potential of the proposed method in terms of identification accuracy and computational efficiency.

Interpretable Hyperspectral Artificial Intelligence: When nonconvex modeling meets hyperspectral remote sensing

“…• Graph 1/2 -NMF [104]: Ω(A) = A 1/2 + tr(ALA ); • Graph TV [106]: Ω(A) = A TV + tr(ALA ). Owing to the powerful data fitting ability, DL-based SU approaches have recently been paid increasing attention and achieved better unmixing results [109]- [112].…”

Graph-Based Active Learning for Nearly Blind Hyperspectral Unmixing

“…We compare our semi-supervised methods with five state-ofthe-art unsupervised unmixing methods, namely, FCLSU [10], GLNMF [26], QMV [20], GTVMBO [30], MSC [35] and EGU [36]. The first three methods (GLNMF, QMV, GTVMBO) initialize with the output of FCLSU [10].…”

“…Graph-based approaches, while powerful, can suffer from intensive computation, particularly when computing pairwise similarity between pixels. Strategies in speeding up the weight computation include the use of superpixels [27] rather than using the entire hyperspectral image and the Nyström method [28] to generate low-rank approximations of the graph Laplacian [29], [30]. Another efficient alternative is the use of sparse weight matrices, such as the K-Nearest Neighbors (KNN) weight matrix [31], [32].…”

Combinatorial Nonnegative Matrix-Tensor Factorization for Hyperspectral Unmixing Using a General $\ell _{q}$ Norm Regularization

“…TV regularization promotes piecewise smoothness in the abundances matrix of the neighboring pixels for the same endmembers. It was firstly introduced in HU by the study of Iordache et al [15] and followed by a series of other studies like double reweighted ℓ 1 minimization with TV regularizer [16], row-sparsity spectral unmixing via total variation (RSSUn-TV) [17], improved collaborative nonnegative matrix factorization and total variation algorithm (ICoNMF-TV) [18], a data-driven graph TV regularization based NMF [19], robust double spatial regularization sparse unmixing (RDSRSU) [20], and a weighted TV regularized blind unmixing (wtvBU) based on the log-exp function [21].…”