To mitigate the impact of mixed pixels in hyperspectral images (HSIs), substantial progress has been made in both model- and deep learning-based unmixing methods. However, issues such as complex computational processes and limited interpretability, hinder the improvement of their unmixing performance. Particularly, unsupervised nonlinear hyperspectral unmixing (HU) remains a great challenge. In this paper, we propose an extended multilinear mixing (EMLM) model-inspired dual-stream network for unsupervised nonlinear HU. Firstly, the alternating direction method of multipliers (ADMM) algorithm for the EMLM-based unmixing problem is unfolded to construct an encoder network. Subsequently, it is connected to a decoder network derived from the EMLM, creating an autoencoder-like network architecture. Secondly, the original HSIs and superpixel-averaging-based coarse HSIs are input into two network branches with identical architectures, respectively, to build a novel weight-sharing dual-stream network. Furthermore, estimates of abundances and nonlinear parameters obtained from the two branches are utilized to formulate local spatial similarity regularizers, enhancing the network’s loss function and effectively improving unmixing accuracy. Finally, experiments conducted on the laboratory-created dataset and real-world datasets validate that the proposed method exhibits superior unmixing performance compared to state-of-the-art methods. In addition, our code is available at: https://github.com/I3ab/EMLM-Net.

Spectral unmixing of hyperspectral images is an important issue in the fields of remote sensing. Jointly exploring the spectral and spatial information embedded in the data is helpful to enhance the consistency between mixing/unmixing models and real scenarios. This paper proposes a graph regularized nonlinear unmixing method based on the recent multilinear mixing model (MLM). The MLM takes account of all orders of interactions between endmembers, and indicates the pixel-wise nonlinearity with a single probability parameter. By incorporating the Laplacian graph regularizers, the proposed method exploits the underlying manifold structure of the pixels’ spectra, in order to augment the estimations of both abundances and nonlinear probability parameters. Besides the spectrum-based regularizations, the sparsity of abundances is also incorporated for the proposed model. The resulting optimization problem is addressed by using the alternating direction method of multipliers (ADMM), yielding the so-called graph regularized MLM (G-MLM) algorithm. To implement the proposed method on large hypersepectral images in real world, we propose to utilize a superpixel construction approach before unmixing, and then apply G-MLM on each superpixel. The proposed methods achieve superior unmixing performances to state-of-the-art strategies in terms of both abundances and probability parameters, on both synthetic and real datasets.

Recently, the research on nonlinear unmixing for hyperspectral images (HSIs) has received more and more attention. However, unsupervised nonlinear unmixing methods that jointly estimate endmembers and abundances from HSIs are insufficiently studied. Besides, the reasonable description of the wavelength-dependent nonlinear intensity and the effective utilization of the spectral and spatial information of HSIs remain to be improved. Based on an extended multilinear mixing model, a coarse-to-fine scheme is proposed for unsupervised nonlinear hyperspectral unmixing to address the above issues. Coarse HSIs generated based on the superpixel segmentation are unmixed first, and then fine unmixing on the original HSIs is achieved with the guidance of the coarse unmixing results. The endmembers extracted by the coarse unmixing are used to update the endmembers in the fine unmixing, and the coarse abundances and nonlinear parameters are integrated into regularizers. To be specific, a weighted sparse regularizer of abundances and a weighted graph regularizer of nonlinear parameters are constructed and incorporated into the objective function. In this way, some priors can be well modeled and exploited, including that the neighboring pixels share similar sparsity patterns in the abundances and show the consistency in correlations between different bands of the nonlinear parameters. Finally, the alternative optimization strategy and the alternating direction method of multipliers are applied to derive the algorithm. Experimental results on the synthetic, laboratory-created, and real hyperspectral data demonstrate that the proposed method outperforms the state-of-the-art nonlinear unmixing methods.

Recently, nonlinear unmixing algorithms have attracted special attention in hyperspectral image (HSI) processing. However, the inherent wavelength-dependent nonlinear intensity and noise effects in real HSIs are often overlooked, and the spatial information of HSIs has not been fully utilized in current studies. In this paper, we propose a spectral-spatial reweighted robust nonlinear unmixing algorithm to solve the above problems. First, a robust unmixing method is built on an extended multilinear mixing model (EMLM), which employs the vectorized nonlinear parameters to describe the nonlinear intensity varying along with spectral bands, and adopts the l _2,1 norm-based loss function to suppress the influence of noise. Second, to fully exploit the spectral-spatial information of HSIs, the nonlinear unmixing problem is reformulated with two regularizers. Specifically, a reweighted collaborative sparse regularizer is used to make the pixels in a superpixel-based neighborhood share the same subset of endmembers and have similar abundances because the neighboring pixels are usually composed of several materials in similar proportions, and a reweighted spectral total variation regularizer is utilized to improve the spectral-spatial smoothness of the vectorized nonlinear parameters by considering the local-region similarities of the nonlinear mixing effects. Finally, the constrained optimization problem is solved by the alternating direction method of multipliers (ADMM). Experimental results on simulated, semi-simulated, and real hyperspectral datasets demonstrate that the proposed method outperforms several state-of-the-art nonlinear unmixing methods.