Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty which simultaneously enforces group and within group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well chosen penalties can significantly improve the unmixing performance compared to classical sparse regression techniques or to the naive bundle approach.

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Scanning probe microscopy (SPM) has facilitated many scientific discoveries utilizing its strengths of spatial resolution, non-destructive characterization and realistic in situ environments. However, accurate spatial data are required for quantitative applications but this is challenging for SPM especially when imaging at higher frame rates. We present a new operation mode for scanning probe microscopy that uses advanced image processing techniques to render accurate images based on position sensor data. This technique, which we call sensor inpainting, frees the scanner to no longer be at a specific location at a given time. This drastically reduces the engineering effort of position control and enables the use of scan waveforms that are better suited for the high inertia nanopositioners of SPM. While in raster scanning, typically only trace or retrace images are used for display, in Archimedean spiral scans 100% of the data can be displayed and at least a two-fold increase in temporal or spatial resolution is achieved. In the new mode, the grid size of the final generated image is an independent variable. Inpainting to a few times more pixels than the samples creates images that more accurately represent the ground truth.

International audienceWe apply social-norms for the first time to the problem of hyperspectral unmixing while modeling spectral variability. These norms are built with inter-group penalties which are combined in a global intra-group penalization that can enforce selection of entire endmember bundles; this results in the selection of a few representative materials even in the presence of large endmembers bundles capturing each material's variability. We demonstrate improvements quantitatively on synthetic data and qualitatively on real data for three cases of social norms: group, elitist, and a fractional social norm, respectively. We find that the greatest improvements arise from using either the group or fractional flavor

We propose a novel method to detect and correct drift in non-raster scanning probe microscopy. In conventional raster scanning drift is usually corrected by subtracting a fitted polynomial from each scan line, but sample tilt or large topographic features can result in severe artifacts. Our method uses self-intersecting scan paths to distinguish drift from topographic features. Observing the height differences when passing the same position at different times enables the reconstruction of a continuous function of drift. We show that a small number of self-intersections is adequate for automatic and reliable drift correction. Additionally, we introduce a fitness function which provides a quantitative measure of drift correctability for any arbitrary scan shape.