Image Decomposition and Separation Using Sparse Representations: An Overview

This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. The idea to morphologically decompose a signal into its building blocks is an important problem in signal processing and has far-reaching applications in science and technology. Starck , proposed a novel decomposition method—morphological component analysis (MCA)—based on sparse representation of signals. MCA assumes that each (monochannel) signal is the linear mixture of several layers, the so-called morphological components, that are morphologically distinct, e.g., sines and bumps. The success of this method relies on two tenets: sparsity and morphological diversity. That is, each morphological component is sparsely represented in a specific transform domain, and the latter is highly inefficient in representing the other content in the mixture. Once such transforms are identified, MCA is an iterative thresholding algorithm that is capable of decoupling the signal content. Sparsity and morphological diversity have also been used as a novel and effective source of diversity for blind source separation (BSS), hence extending the MCA to multichannel data. Building on these ingredients, we will provide an overview the generalized MCA introduced by the authors in and as a fast and efficient BSS method. We will illustrate the application of these algorithms on several real examples. We conclude our tour by briefly describing our software toolboxes made available for download on the Internet for sparse signal and image decomposition and separation

Evidence for sub-Chandrasekhar-mass progenitors of Type Ia supernovae at the faint end of the width-luminosity relation

The faster light-curve evolution of low-luminosity Type Ia supernovae (SNe Ia) suggests that they could result from the explosion of white dwarf (WD) progenitors below the Chandrasekhar mass ($M_{\rm Ch}$). Here we present 1D non-LTE time-dependent radiative transfer simulations of pure central detonations of carbon-oxygen WDs with a mass (M_\rm{tot}) between 0.88 M$_{\odot}$ and 1.15 M$_{\odot}$, and a $^{56}\rm{Ni}$ yield between 0.08 M$_{\odot}$ and 0.84 M$_{\odot}$. Their lower ejecta density compared to $M_{\rm Ch}$ models results in a more rapid increase of the luminosity at early times and an enhanced $\gamma$-ray escape fraction past maximum light. Consequently, their bolometric light curves display shorter rise times and larger post-maximum decline rates. Moreover, the higher M(^{56}\rm{Ni})/M_\rm{tot} ratio at a given $^{56}\rm{Ni}$ mass enhances the temperature and ionization level in the spectrum-formation region for the less luminous models, giving rise to bluer colours at maximum light and a faster post-maximum evolution of the $B-V$ colour. For sub-$M_{\rm Ch}$ models fainter than $M_B\approx -18.5$ mag at peak, the greater bolometric decline and faster colour evolution lead to a larger $B$-band post-maximum decline rate, $\Delta M_{15}(B)$. In particular, all of our previously-published $M_{\rm Ch}$ models (standard and pulsational delayed detonations) are confined to $\Delta M_{15}(B) < 1.4$ mag, while the sub-$M_{\rm Ch}$ models with M_\rm{tot}\lesssim 1 M$_{\odot}$ extend beyond this limit to $\Delta M_{15}(B)\approx 1.65$ mag for a peak $M_B\approx -17$ mag, in better agreement with the observed width-luminosity relation (WLR). Regardless of the precise ignition mechanism, these simulations suggest that fast-declining SNe Ia at the faint end of the WLR could result from the explosion of WDs whose mass is significantly below the Chandrasekhar limit.Comment: 10 pages, 6 figures. Accepted for publication in MNRA

Genetic diversity and phylogeography of wild-sown and cultivated coconuts (Cocos nucifera L.)

The coconut (Cocos nucifera L.) is a pantropical strand plant, colonizing sandy insular beaches in the humid tropics. Cocos is a monotypic genus in the Cocoseae tribe (18/ca. 200 spp.) within the Arecaceae family. Phylogenetic studies support its sister relationship to Syagrus, a Neotropical genus, sharing a common ancestor about 35 MYBP, though the crown group age of Cocos is about 11 MYBP. Fossil evidence indicates that members of the Cocos lineage were present in South America, India, New Zealand and Australia. Coconuts are adapted to drift-dispersal by ocean currents; however, human activities both historically and today have also aided its spread and impacted its phenotypic and genetic structure. Coconuts are traditionally classified as 'Talls' or 'Dwarfs' based on tree habit. Morphological examination reveal two predominant fruit types, attributed to Polynesian terminology: niu kafa are characterized by their elongated, triangular fruits with large proportion of fibrous husk and niu vai, whose fruits are rounded with large proportion of liquid endosperm. The niu kafa form is interpreted as the naturally evolved coconut, under natural selection for dissemination by sea currents whilst the niu vai form evolved from domestication under human selection for greater volume of delicious coconut water. Here we investigate the genetic diversity of coconuts, the impact of domestication, introgression and the taxonomic implications for this species. We used polymorphic microsatellite markers on 1322 coconut samples representing phenotypic and genetic variation worldwide to examine the geographical location of the center(s) of domestication and its progenitors. Bayesian analyses of population structure revealed two major subpopulations corresponding to the Pacific and Indo-Atlantic oceanic regions. Haplotype networks based on chloroplast and nuclear markers are used as a complementary dataset to examine the coconut's phylogeography. (Texte intégral

A uniform isotopic and chemical signature of dust exported from Patagonia: Rock sources and occurrence in southern environments

Patagonia is considered to be the most important source of dust from South America that is deposited in surrounding areas, and we present here a systematic Sr and Nd isotopic study of sediment currently being exported. Eolian and suspended riverine sediments from Patagonia have a homogeneous chemical and isotopic composition that results from the mixing of by-products from explosive Andean volcanism, derived from the extensive Jurassic silicic Province of Chon Aike and pyroclastic materials from the basic to intermediate southern Andean Quaternary arc, which are easily denudated and dispersed. The main Andean uplift and the glaciations that began in the Late Tertiary account for the extensive distribution of these sediments in the extra-Andean region. The present geochemical signature of Patagonian sediments was produced during the Pleistocene, along with the onset of the southern Andean explosive arc volcanism. Previously published compositions of sediments from other southern South American source regions, assumed to be representative of Patagonia, are distinct from our data. Considering the alleged importance of Patagonia as a dust source for different depositional environments in southern latitudes, it is surprising to verify that the chemical and isotopic signatures of Patagonian-sourced sediments are different from those of sediments from the Southern Ocean, the Pampean Region or the Antarctic ice. Sediments from these areas have a crustal-like geochemical signature reflecting a mixed origin with sediment from other southern South American sources, whereas Patagonian sediments likely represent the basic to intermediate end-member composition

Ellerman Bombs at high resolution: II. Visibility, triggering and effect on upper atmosphere

We use high-resolution imaging spectroscopy with the Swedish 1-m Solar Telescope (SST) to study the transient brightenings of the wings of the Balmer Halpha line in emerging active regions that are called Ellerman bombs. Simultaneous sampling of Ca II 854.2 nm with the SST confirms that most Ellerman bombs occur also in the wings of this line, but with markedly different morphology. Simultaneous images from the Solar Dynamics Observatory (SDO) show that Ellerman bombs are also detectable in the photospheric 170 nm continuum, again with differing morphology. They are also observable in 160 nm SDO images, but with much contamination from C IV emission in transition-region features. Simultaneous SST spectropolarimetry in Fe I 630.1 nm shows that Ellerman bombs occur at sites of strong-field magnetic flux cancelation between small bipolar strong-field patches that rapidly move together over the solar surface. Simultaneous SDO images in He II 30.4 nm, Fe IX 17.1 nm, and Fe XIV 21.1 nm show no clear effect of the Ellerman bombs on the overlying transition region and corona. These results strengthen our earlier suggestion, based on Halpha morphology alone, that the Ellerman bomb phenomenon is a purely photospheric reconnection phenomenon.Comment: Accepted for publication in The Astrophysical Journal. 16 pages, 10 figure

Evidence for a Transition Region response to penumbral microjets in sunspots

Penumbral microjets are short-lived, fine-structured and bright jets that are generally observed in chromospheric imaging of the penumbra of sunspots. Here we investigate their potential transition region signature, by combining observations with the Swedish 1-m Solar Telescope (SST) in the Ca II H and Ca II 8542{\AA} lines with ultraviolet imaging and spectroscopy obtained with the Interface Region Imaging Spectrograph (IRIS), which includes the C II 1334/1335{\AA}, Si IV 1394/1403{\AA} and Mg II h & k 2803/2796{\AA} lines. We find a clear corresponding signal in the IRIS Mg II k, C II and Si IV slit-jaw images, typically offset spatially from the Ca II signature in the direction along the jets: from base to top, the penumbral microjets are predominantly visible in Ca II, Mg II k and C II/Si IV, suggesting progressive heating to transition region temperatures along the jet extent. Hence, these results support the suggestion from earlier studies that penumbral microjets may heat to transition region temperatures.Comment: Accepted for publication in the Astrophysical Journal Letters. 6 pages, 5 figure

A model for the continuous q-ultraspherical polynomials

We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q$-Heisenberg algebra and a $q$-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous $q$-Hermite polynomials and a $q$-analog of the Fourier-Gegenbauer expansion are naturally obtained from these models