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Formulated as a least square problem under an ℓ 0 constraint, sparse signal restoration is a discrete optimization problem, known to be NP complete. Classical algorithms include, by increasing cost and efficiency, Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), Orthogonal Least Squares (OLS), stepwise regression algorithms and the exhaustive search. We revisit the Single Most Likely Replacement (SMLR) algorithm, developed in the mid-80's for Bernoulli-Gaussian signal restoration. We show that the formulation of sparse signal restoration as a limit case of Bernoulli-Gaussian signal restoration leads to an ℓ 0-penalized least square minimization problem, to which SMLR can be straightforwardly adapted. The resulting algorithm, called Single Best Replacement (SBR), can be interpreted as a forward-backward extension of OLS sharing similarities with stepwise regression algorithms. Some structural properties of SBR are put forward. A fast and stable implementation is proposed. The approach is illustrated on two inverse problems involving highly correlated dictionaries. We show that SBR is very competitive with popular sparse algorithms in terms of trade-off between accuracy and computation time.

Atomic force microscopy (AFM) has now become a powerful technique for investigating on a molecular level, surface forces, nanomechanical properties of deformable particles, biomolecular interactions, kinetics, and dynamic processes. This paper specifically focuses on the analysis of AFM force curves collected on biological systems, in particular, bacteria. The goal is to provide fully automated tools to achieve theoretical interpretation of force curves on the basis of adequate, available physical models. In this respect, we propose two algorithms, one for the processing of approach force curves and another for the quantitative analysis of retraction force curves. In the former, electrostatic interactions prior to contact between AFM probe and bacterium are accounted for and mechanical interactions operating after contact are described in terms of Hertz-Hooke formalism. Retraction force curves are analyzed on the basis of the Freely Jointed Chain model. For both algorithms, the quantitative reconstruction of force curves is based on the robust detection of critical points (jumps, changes of slope or changes of curvature) which mark the transitions between the various relevant interactions taking place between the AFM tip and the studied sample during approach and retraction. Once the key regions of separation distance and indentation are detected, the physical parameters describing the relevant interactions operating in these regions are extracted making use of regression procedure for fitting experiments to theory. The flexibility, accuracy and strength of the algorithms are illustrated with the processing of two force-volume images, which collect a large set of approach and retraction curves measured on a single biological surface. For each force-volume image, several maps are generated, representing the spatial distribution of the searched physical parameters as estimated for each pixel of the force-volume image.

The surface of Mars is currently being imaged with an unprecedented combination of spectral and spatial resolution. This high resolution, and its spectral range, give the ability to pinpoint chemical species on the surface and the atmosphere of Mars moreaccurately than before. The subject of this paper is to present a method to extract informations on these chemicals from hyperspectral images. A first approach, based on Independent Component Analysis (ICA) [1], is able to extract artifacts and locations of CO2 and H2O ices. However, the main independence assumption and some basic properties (like the positivity of images and spectra) being unverified, the reliability of all the independent components (ICs) is weak. For improving the component extraction and consequently the endmember classification, a combination of spatial ICA with spectral Bayesian Positive Source Separation (BPSS) [2] is proposed. To reduce the computational burden, the basic idea is to use spatial ICA yielding a rough classification of pixels, which allows selection of small, but relevant, number of pixels and then BPSS is applied for the estimation of the source spectra using the spectral mixtures provided by this reduced set of pixels. Finally, the abundances of the components is assessed on the whole pixels of the images. Results of this approach are shown and evaluated by comparison with available reference spectra.

We propose a novel approach for hyperspectral super-resolution, that is based on low-rank tensor approximation for a coupled low-rank multilinear (Tucker) model. We show that the correct recovery holds for a wide range of multilinear ranks. For coupled tensor approximation, we propose two SVD-based algorithms that are simple and fast, but with a performance comparable to the state-of-the-art methods. The approach is applicable to the case of unknown spatial degradation and to the pansharpening problem.

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Aim To reconstruct the spatio‐temporal evolution of Fosterella (Bromeliaceae), a genus characterized by a high degree of endemism in the Central Andes, and to account for contemporary patterns of diversity and distribution within the genus. Location Fosterella has its centre of diversity in the Central Andes (24 species), where it occurs in two major biomes: the Yungas and seasonally dry tropical forests (SDTF). The genus displays three major disjunctions: Amazonia (one species), Central America (one species), and the Brazilian Shield (five species). Methods Phylogenetic relationships within Fosterella were inferred based on six plastid DNA regions. Parsimony and likelihood methods, a Bayesian relaxed molecular clock, ancestral area reconstructions, and diversification rate analyses were used to infer the spatio‐temporal evolution of Fosterella. Results The origin of extant lineages of Fosterella was placed in the late Miocene (c. 9.6 Ma) during the last rapid Andean uplift. SDTF and azonal lowland sites were inferred as the most likely ancestral habitats. The Yungas were colonized several times independently from c. 4.7 Ma onwards. Only one clade diversified in the Yungas, indicative of an ecological shift to moister and cooler conditions. Two recent long‐distance dispersals to Central America and to Amazonia were inferred. Diversification rates within Fosterella were found to be constant through time and comparatively low (0.4 species Myr−1). Main conclusions Allopatric speciation is the main mode of diversification in Fosterella. The isolated distribution of suitable habitats fostered the evolution of a high degree of endemism. The low speciation rates in Fosterella contrast with high diversification rates of Andean high‐elevation taxa but are similar to other Andean low‐ to mid‐elevation taxa. The last rapid Andean uplift did not leave a detectable signature in the diversification rates of Fosterella.