Region-Based Structure Preserving Nonnegative Matrix Factorization for Hyperspectral Unmixing

Abstract

Hyperspectral unmixing is one of the most important techniques in remote sensing image analysis. In recent years, nonnegative matrix factorization (NMF) method is widely used in hyperspectral unmixing. In order to solve the nonconvex problem of NMF method, a number of constraints have been introduced into NMF models, including sparsity, manifold, smoothness, et al. However, these constraints ignore an important property of hyperspectral image, i.e., the spectral responses in a homogeneous region are similar at each pixel but vary in different homogeneous regions. In this paper. We introduce a novel region based structure preserving NMF (R-NMF) to explore consistent data distribution in the same region while discriminating different data structures across regions in the unmixed data. In this method, a graph cut algorithm is first applied to segment the hyperspectral image to small homogeneous regions. Then two constraints are applied to the unmixing model, which preserve the structural consistency within region while discriminating the differences between regions. Results on both synthetic and real data have validated the effectiveness of this method, and shown that it has outperformed several state-of-theart unmixing approaches.

Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization

“…In order to obtain more accurate results, additional physical constraints on endmembers or abundances should be incorporated into the objective function besides the ANC and ASC [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Consistent with the idea of using minimum-volume-constrained NMF for unmixing highly mixed data [11,12], ∆ r−1 spanned by endmembers {a 1 , a 2 , .…”

“…NMF is usually adopted for solving the blind source separation (BSS) problem, but the cost function's non-convexity impedes its direct use in unsupervised unmixing. Therefore, besides the volume constraints, various physical constraints have also been designed and incorporated into the NMF framework to mitigate the problem of local minima and obtain better unmixing results [14][15][16][17][18][19][20][21][22][23][24][25]. For instance, a smoothness constraint was adopted in [16,17], and spatial information of the data manifold was exploited in [18,19] to construct the constraints.…”

“…Therefore, besides the volume constraints, various physical constraints have also been designed and incorporated into the NMF framework to mitigate the problem of local minima and obtain better unmixing results [14][15][16][17][18][19][20][21][22][23][24][25]. For instance, a smoothness constraint was adopted in [16,17], and spatial information of the data manifold was exploited in [18,19] to construct the constraints. Moreover, some algorithms have also provided promising unmixing results by combining the sparsity with other constraints to reformulate the optimization problem of NMF [20][21][22][23][24][25].…”

When remote sensing meets topological data analysis

“…all the available pixels or just a cropped version of it. [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] In our case, the whole data set of almost 400,000 pixels has been used to show the good scalability of the proposed concept.…”

Bilateral Filter Regularized L2 Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing

“…Moreover, some of the algorithms attempt to utilize the internal structural information of HSI and suppose that similar pixels correspond to similar abundances, such as graph-regularized L 1/2 -NMF (GLNMF) [35], structured sparse NMF (SS-NMF) [36], and hypergraph-regularized L 1/2 -NMF (HG L 1/2 -NMF) [37], which are all based on the graph Laplacian constraint [38]. In [39] and [40], however, the structural information is adopted by clustering and region segmentation, and the mean abundance of each class or region is computed so as to keep the abundance vectors similar.…”