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Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing and communications applications, including denoising, spectrum sensing, and compression. Notice that estimating the covariance matrix from compressive samples leads to ill-posed minimizations with severe performance loss at high compression rates. In this regard, a regularization term is typically aggregated to the cost function to consider prior information about a particular property of the covariance matrix. Hence, this paper proposes an algorithm based on the projected gradient method to recover low-rank or Toeplitz approximations of the covariance matrix from compressive measurements. The proposed algorithm divides the compressive measurements into data subsets projected onto different subspaces and accurately estimates the covariance matrix by solving a single optimization problem assuming that each data subset contains an approximation of the signal statistics. Furthermore, gradient filtering is included at every iteration of the proposed algorithm to minimize the estimation error. The error induced by the proposed splitting approach is analytically derived along with the convergence guarantees of the proposed method. The proposed algorithm estimates the covariance matrix of hyperspectral images from synthetic and real compressive samples. Extensive simulations show that the proposed algorithm can effectively recover the covariance matrix of hyperspectral images from compressive measurements with high compression ratios ($8-15\%$ approx) in noisy scenarios. Moreover, simulations and theoretical results show that the filtering step reduces the recovery error up to twice the number of eigenvectors. Finally, an optical implementation is proposed, and real measurements are used to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images. [ABSTRACT FROM AUTHOR]

Due to hardware limitations of the imaging sensors, it is challenging to acquire images of high resolution in both spatial and spectral domains. Fusing a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to obtain an HR-HSI in an unsupervised manner has drawn considerable attention. Though effective, most existing fusion methods are limited due to the use of linear parametric modeling for the spectral mixture process, and even the deep learning-based methods only focus on deterministic fully-connected networks without exploiting the spatial correlation and local spectral structures of the images. In this paper, we propose a novel variational probabilistic autoencoder framework implemented by convolutional neural networks, in order to fuse the spatial and spectral information contained in the LR-HSI and HR-MSI, called FusionNet. The FusionNet consists of a spectral generative network, a spatial-dependent prior network, and a spatial-spectral variational inference network, which are jointly optimized in an unsupervised manner, leading to an end-to-end fusion system. Further, for fast adaptation to different observation scenes, we give a meta-learning explanation to the fusion problem, and combine the FusionNet with meta-learning in a synergistic manner. Effectiveness and efficiency of the proposed method are evaluated based on several publicly available datasets, demonstrating that the proposed FusionNet outperforms the state-of-the-art fusion methods. [ABSTRACT FROM AUTHOR]

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm. [ABSTRACT FROM PUBLISHER]

The main problems in hyperspectral image analysis are spectral classification, segmentation, and data reduction. In this paper, we propose a Bayesian estimation approach which gives a joint solution for these problems. The problem is modeled as a blind sources separation (BSS). The data are M hyperspectral images and the sources are K < M images which are composed of compact homogeneous regions and have mutually disjoint supports. The set of all these regions cover the total surface of the observed scene. To insure these properties, we propose a hierarchical Markov model for the sources with a common hidden classification field which is modeled via a Potts-Markov field. The joint Bayesian estimation of the hidden variable, sources, and the mixing matrix of the BSS gives a solution for all three problems: spectra classification, segmentation, and data reduction of hyperspectral images. The mean field approximation (MFA) algorithm for the posterior laws is proposed for the effective Bayesian computation. Finally, some results of the application of the proposed methods on simulated and real data are given to illustrate the performance of the proposed method compared to other classical methods, such as PCA and ICA. [ABSTRACT FROM AUTHOR]

This paper presents a novel support vector machine classifier designed for subpixel image classification (pixel/spectral unmixing). The proposed classifier generalizes the properties of SVMs to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic. This results in the definition of a fuzzy-input fuzzy-output support vector machine (F^2SVM) classifier that can: 1) process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2) provide a fuzzy modeling of the classification results, allowing a relation many-to-one between classes and pixels. The presented binary F^2SVM can address multicategory problems according to two strategies: the fuzzy one-against-all (FOAA) and the fuzzy one-against-one (FOAO) strategies. These strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems. The effectiveness of the proposed F^2SVM classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics. Experimental results confirm the validity of the proposed subpixel classification method. [ABSTRACT FROM PUBLISHER]

In this brief, we provide an efficient scheme for performing deconvolution of large hyperspectral images under a positivity constraint, while accounting for spatial and spectral smoothness of the data. [ABSTRACT FROM PUBLISHER]

Semi-implicit schemes have been recently shown to speed up nonlinear diffusion in hyperspectral images while increasing the accuracy of subsequent classifiers in thematic mapping. Here, we show how semi-implicit schemes can be used to implement a truly anisotropic diffusion method for hyperspectral images, and we test the performance of different implementations in terms of computational overhead, speed, numerical accuracy, and thematic mapping performance. In addition, truly anisotropic trace-based diffusion formulations, besides a more precise steering of the diffusion processes, also allow implementation by means of local oriented Gaussian masks. We show how the implementations with the highest numerical accuracy can be also the simplest and fastest while still increasing the classification performance. [ABSTRACT FROM PUBLISHER]