Dynamical spectral unmixing of multitemporal hyperspectral images

In this paper, we consider the problem of unmixing a time series of hyperspectral images. We propose a dynamical model based on linear mixing processes at each time instant. The spectral signatures and fractional abundances of the pure materials in the scene are seen as latent variables, and assumed to follow a general dynamical structure. Based on a simplified version of this model, we derive an efficient spectral unmixing algorithm to estimate the latent variables by performing alternating minimizations. The performance of the proposed approach is demonstrated on synthetic and real multitemporal hyperspectral images.Comment: 13 pages, 10 figure

A Framework for Fast Image Deconvolution with Incomplete Observations

In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods, or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. In this paper, we propose a new deconvolution framework for images with incomplete observations that allows us to work with diagonalized convolution operators, and therefore is very fast. We iteratively alternate the estimation of the unknown pixels and of the deconvolved image, using, e.g., an FFT-based deconvolution method. This framework is an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge tapering. It can be used with any fast deconvolution method. We give an example in which a state-of-the-art method that assumes periodic boundary conditions is extended, through the use of this framework, to unknown boundary conditions. Furthermore, we propose a specific implementation of this framework, based on the alternating direction method of multipliers (ADMM). We provide a proof of convergence for the resulting algorithm, which can be seen as a "partial" ADMM, in which not all variables are dualized. We report experimental comparisons with other primal-dual methods, where the proposed one performed at the level of the state of the art. Four different kinds of applications were tested in the experiments: deconvolution, deconvolution with inpainting, superresolution, and demosaicing, all with unknown boundaries.Comment: IEEE Trans. Image Process., to be published. 15 pages, 11 figures. MATLAB code available at https://github.com/alfaiate/DeconvolutionIncompleteOb

A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe

Collaborative Sliced Inverse Regression

International audienceSliced Inverse Regression (SIR) is an effective method for dimensionality reduction in high-dimensional regression problems. However, the method has requirements on the distribution of the predictors that are hard to check since they depend on unobserved variables. It has been shown that, if the distribution of the predictors is elliptical, then these requirements are satisfied.In case of mixture models, the ellipticity is violated and in addition there is no assurance of a single underlying regression model among the different components. Our approach clusterizes the predictors space to force the condition to hold on each cluster and includes a merging technique to look for different underlying models in the data. A study on simulated data as well as two real applications are provided. It appears that SIR, unsurprisingly, is not capable of dealing with a mixture of Gaussians involving different underlying models whereas our approach is able to correctly investigate the mixture

Variability of the endmembers in spectral unmixing: recent advances

International audienceEndmember variability has been identified as one of the main limitations of the usual Linear Mixing Model, conventionally used to perform spectral unmixing of hyperspectral data. The topic is currently receiving a lot of attention from the community, and many new algorithms have recently been developed to model this variability and take it into account. In this paper, we review state of the art methods dealing with this problem and classify them into three categories: the algorithms based on endmember bundles, the ones based on computational models, and the ones based on parametric physics-based models. We discuss the advantages and drawbacks of each category of methods and list some open problems and current challenges

Segmentation hiérarchique d'images multimodales

National audienceHierarchies of partitions are widely used in the context of image segmentation. However,in the case of multimodal images, the fusion of multiple hierarchies remains a challenge. Recently, braids of partitions have been proposed as a possible solution to this issue, but have never been implemented in a practical case.In this paper, we propose a new methodology to achieve multimodal segmentation, based on this notion of braids of partitions. This new method is applied in a practical case, namely the joint segmentation of hyperspectral and LiDAR data. Obtained results confirm the potential of the proposed method.Les hiérarchies de partitions sont couramment utilisées pour segmentation d'images. Dans le cas d'images multimodales toutefois, la fusion de plusieurs hiérarchies reste un problème. Récemment, les tresses de partitions ont été proposées comme une possible solution à ce problème, mais n'ont jamais été implémentées dans un cas pratique. Nous proposons ainsi une nouvelle méthodologie, basée sur cette notion de tresse de partitions, pour effectuer la segmentation d'images multimodales. Cette méthode est appliquée dans un cas concret, à savoir la segmentation conjointe de données hyperspectrales et LiDAR. Les résultats obtenus confirment le potentiel de la méthode proposée

Fourier-based Rotation-invariant Feature Boosting: An Efficient Framework for Geospatial Object Detection

Geospatial object detection of remote sensing imagery has been attracting an increasing interest in recent years, due to the rapid development in spaceborne imaging. Most of previously proposed object detectors are very sensitive to object deformations, such as scaling and rotation. To this end, we propose a novel and efficient framework for geospatial object detection in this letter, called Fourier-based rotation-invariant feature boosting (FRIFB). A Fourier-based rotation-invariant feature is first generated in polar coordinate. Then, the extracted features can be further structurally refined using aggregate channel features. This leads to a faster feature computation and more robust feature representation, which is good fitting for the coming boosting learning. Finally, in the test phase, we achieve a fast pyramid feature extraction by estimating a scale factor instead of directly collecting all features from image pyramid. Extensive experiments are conducted on two subsets of NWPU VHR-10 dataset, demonstrating the superiority and effectiveness of the FRIFB compared to previous state-of-the-art methods