Abstract
Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due to its good adaptability for mixed data with different degrees. The majority of existing NMF-based unmixing methods are developed by incorporating additional constraints into the standard NMF based on the spectral and spatial information of hyperspectral images. However, they neglect to exploit the nature of imbalanced pixels included in the data, which may cause the pixels mixed with imbalanced endmembers to be ignored, and thus the imbalanced endmembers generally cannot be accurately estimated due to the statistical property of NMF. To exploit the information of imbalanced samples in hyperspectral data during the unmixing procedure, in this paper, a cluster-wise weighted NMF (CW-NMF) method for the unmixing of hyperspectral images with imbalanced data is proposed. Specifically, based on the result of clustering conducted on the hyperspectral image, we construct a weight matrix and introduce it into the model of standard NMF. The proposed weight matrix can provide an appropriate weight value to the reconstruction error between each original pixel and the reconstructed pixel in the unmixing procedure. In this way, the adverse effect of imbalanced samples on the statistical accuracy of NMF is expected to be reduced by assigning larger weight values to the pixels concerning imbalanced endmembers and giving smaller weight values to the pixels mixed by majority endmembers. Besides, we extend the proposed CW-NMF by introducing the sparsity constraints of abundance and graph-based regularization, respectively. The experimental results on both synthetic and real hyperspectral data have been reported, and the effectiveness of our proposed methods has been demonstrated by comparing them with several state-of-the-art methods.
Highlights
We focus on improving the unmixing accuracy of the standard negative matrix factorization (NMF) on sample number related imbalanced data, in which the endmembers included by a relatively small number of pixels are named imbalanced endmembers, and the ones included by a large number of pixels are named majority endmembers
When our methods are tested on real hyperspectral data, they are compared with four representative algorithms, i.e., NMF, L1/2 NMF, graph regularized L1/2 NMF (GLNMF), spatial group sparsity regularized NMF (SGSNMF), and Vertex Component Analysis (VCA) followed by FCLS (VCA-FCLS), in which the first four are NMF-based unmixing methods, whereas VCA is a famous geometry-based method for endmember extraction
We have proposed a cluster-wise weighted NMF method for hyperspectral unmixing by exploiting the information of imbalanced samples in hyperspectral images
Summary
The spectra of pixels in real HSIs may be mixtures of several pure spectral signatures (i.e., endmembers) corresponding to different substances. This is commonly caused by the limited spatial resolution of the sensors and the complex distribution of land cover materials. To enhance the analysis accuracy of hyperspectral images in practical applications, hyperspectral unmixing (HU) [5], which aims to decompose each mixed pixel in an HSI into a set of endmembers and their corresponding proportions (i,e., abundances), has become a hot research topic [6,7]. Due to its simplicity and interpretability, LMM is widely adopted in practical applications [9]
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