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Register a new userMatrix cofactorization for joint spatial-spectral unmixing of hyperspectral images
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Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often very correlated yielding an ill-conditioned problem. To enrich the model and to reduce ambiguity due to the high correlation, it is common to introduce spatial information to complement the spectral information. The most common way to introduce spatial information is to rely on a spatial regularization of the abundance maps. In this paper, instead of considering a simple but limited regularization process, spatial information is directly incorporated through the newly proposed context of spatial unmixing. Contextual features are extracted for each pixel and this additional set of observations is decomposed according to a linear model. Finally the spatial and spectral observations are unmixed jointly through a cofactorization model. In particular, this model introduces a coupling term used to identify clusters of shared spatial and spectral signatures. An evaluation of the proposed method is conducted on synthetic and real data and shows that results are accurate and also very meaningful since they describe both spatially and spectrally the various areas of the scene.
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Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this paper, a method coupling these two approaches is designed using a matrix cofactorization formulation. Each task is modeled as a factorization matrix problem and a term relating both coding matrices is then introduced to drive an appropriate coupling. The link can be interpreted as a clustering operation over a low-dimensional representation vectors. The attribution vectors of the clustering are then used as features vectors for the classification task, i.e., the coding vectors of the corresponding factorization problem. A proximal gradient descent algorithm, ensuring convergence to a critical point of the objective function, is then derived to solve the resulting non-convex non-smooth optimization problem. An evaluation of the proposed method is finally conducted both on synthetic and real data in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification.
Tensor-based methods have been widely studied to attack inverse problems in hyperspectral imaging since a hyperspectral image (HSI) cube can be naturally represented as a third-order tensor, which can perfectly retain the spatial information in the image. In this article, we extend the linear tensor method to the nonlinear tensor method and propose a nonlinear low-rank tensor unmixing algorithm to solve the generalized bilinear model (GBM). Specifically, the linear and nonlinear parts of the GBM can both be expressed as tensors. Furthermore, the low-rank structures of abundance maps and nonlinear interaction abundance maps are exploited by minimizing their nuclear norm, thus taking full advantage of the high spatial correlation in HSIs. Synthetic and real-data experiments show that the low rank of abundance maps and nonlinear interaction abundance maps exploited in our method can improve the performance of the nonlinear unmixing. A MATLAB demo of this work will be available at https://github.com/LinaZhuang for the sake of reproducibility.
The direct detection of exoplanets with high-contrast instruments can be boosted with high spectral resolution. For integral field spectrographs yielding hyperspectral data, this means that the field of view consists of diffracted starlight spectra and a spatially localized planet. Analysis usually relies on cross-correlation with theoretical spectra. In a purely blind-search context, this supervised strategy can be biased with model mismatch and/or be computationally inefficient. Using an approach that is inspired by the remote-sensing community, we aim to propose an alternative to cross-correlation that is fully data-driven, which decomposes the data into a set of individual spectra and their corresponding spatial distributions. This strategy is called spectral unmixing. We used an orthogonal subspace projection to identify the most distinct spectra in the field of view. Their spatial distribution maps were then obtained by inverting the data. These spectra were then used to break the original hyperspectral images into their corresponding spatial distribution maps via non-negative least squares. The performance of our method was evaluated and compared with a cross-correlation using simulated hyperspectral data with medium resolution from the ELT/HARMONI integral field spectrograph. We show that spectral unmixing effectively leads to a planet detection solely based on spectral dissimilarities at significantly reduced computational cost. The extracted spectrum holds significant signatures of the planet while being not perfectly separated from residual starlight. The sensitivity of the supervised cross-correlation is three to four times higher than with unsupervised spectral unmixing, the gap is biased toward the former because the injected and correlated spectrum match perfectly. The algorithm was furthermore vetted on real data obtained with VLT/SINFONI of the beta Pictoris system.
Clustering algorithms partition a dataset into groups of similar points. The primary contribution of this article is the Multiscale Spatially-Regularized Diffusion Learning (M-SRDL) clustering algorithm, which uses spatially-regularized diffusion distances to efficiently and accurately learn multiple scales of latent structure in hyperspectral images (HSI). The M-SRDL clustering algorithm extracts clusterings at many scales from an HSI and outputs these clusterings variation of information-barycenter as an exemplar for all underlying cluster structure. We show that incorporating spatial regularization into a multiscale clustering framework corresponds to smoother and more coherent clusters when applied to HSI data and leads to more accurate clustering labels.
In this paper, we propose a spectral-spatial graph reasoning network (SSGRN) for hyperspectral image (HSI) classification. Concretely, this network contains two parts that separately named spatial graph reasoning subnetwork (SAGRN) and spectral graph reasoning subnetwork (SEGRN) to capture the spatial and spectral graph contexts, respectively. Different from the previous approaches implementing superpixel segmentation on the original image or attempting to obtain the category features under the guide of label image, we perform the superpixel segmentation on intermediate features of the network to adaptively produce the homogeneous regions to get the effective descriptors. Then, we adopt a similar idea in spectral part that reasonably aggregating the channels to generate spectral descriptors for spectral graph contexts capturing. All graph reasoning procedures in SAGRN and SEGRN are achieved through graph convolution. To guarantee the global perception ability of the proposed methods, all adjacent matrices in graph reasoning are obtained with the help of non-local self-attention mechanism. At last, by combining the extracted spatial and spectral graph contexts, we obtain the SSGRN to achieve a high accuracy classification. Extensive quantitative and qualitative experiments on three public HSI benchmarks demonstrate the competitiveness of the proposed methods compared with other state-of-the-art approaches.
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