The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no longer valid in the presence of intra-class variability due to illumination conditions, weathering, slight variations of the pure materials, etc. In this paper, we first describe the results of investigations highlighting intra-class variability measured in real images. Considering these results, a new formulation of the linear mixing model is presented leading to two new methods. Unconstrained pixel-by-pixel NMF (UP-NMF) is a new blind source separation method based on the assumption of a linear mixing model, which can deal with intra-class variability. To overcome the limitations of UP-NMF, an extended method is also proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each sensed spectrum, these extended versions of NMF extract a corresponding set of source spectra. A constraint is set to limit the spreading of each source’s estimates in IP-NMF. The proposed methods are first tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and then numerically mixed. We thus demonstrate the interest of our methods for realistic source variabilities. Finally, IP-NMF is tested on a real data set and it is shown to yield better performance than state of the art methods.

High-spectral-resolution hyperspectral data are acquired by sensors that gather images from hundreds of narrow and contiguous bands of the electromagnetic spectrum. These data offer unique opportunities for characterization and precise land surface recognition in urban areas. So far, few studies have been conducted with these data to automatically detect and estimate areas of photovoltaic panels, which currently constitute an important part of renewable energy systems in urban areas of developed countries. In this paper, two hyperspectral-unmixing-based methods are proposed to detect and to estimate surfaces of photovoltaic panels. These approaches, related to linear spectral unmixing (LSU) techniques, are based on new nonnegative matrix factorization (NMF) algorithms that exploit known panel spectra, which makes them partial NMF methods. The first approach, called Grd-Part-NMF, is a gradient-based method, whereas the second one, called Multi-Part-NMF, uses multiplicative update rules. To evaluate the performance of these approaches, experiments are conducted on realistic synthetic and real airborne hyperspectral data acquired over an urban region. For the synthetic data, obtained results show that the proposed methods yield much better overall performance than NMF-unmixing-based methods from the literature. For the real data, the obtained detection and area estimation results are first confirmed by using very high-spatial-resolution ortho-images of the same regions. These results are also compared with those obtained by standard NMF-unmixing-based methods and by a one-class-classification-based approach. This comparison shows that the proposed approaches are superior to those considered from the literature.

Hypersharpening aims at combining an observable low-spatial resolution hyperspectral image with a high-spatial resolution remote sensing image, in particular a multispectral one, to generate an unobservable image with the high spectral resolution of the former and the high spatial resolution of the latter. In this paper, two such new fusion methods are proposed. These methods, related to linear spectral unmixing techniques, and based on nonnegative matrix factorization (NMF), optimize a new joint criterion and extend the recently proposed joint NMF (JNMF) method. The first approach, called gradient-based joint-criterion NMF (Grd-JCNMF), is a gradient-based method. The second one, called multiplicative JCNMF (Mult-JCNMF), uses new designed multiplicative update rules. These two JCNMF approaches are applied to synthetic and semireal data, and their effectiveness, in spatial and spectral domains, is evaluated with commonly used performance criteria. Experimental results show that the proposed JCNMF methods yield sharpened hyperspectral data with good spectral and spatial fidelities. The obtained results are compared with the performance of two NMF-based methods and one approach based on a sparse representation. These results show that the proposed methods significantly outperform the well-known coupled NMF sharpening method for most performance figures. Also, the proposed Mult-JCNMF method provides the results that are similar to those obtained by JNMF, with a lower computational cost. Compared with the tested sparse-representation-based approach, the proposed methods give better results. Moreover, the proposed Grd-JCNMF method considerably surpasses all other tested methods.