Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization

We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. Many popular greedy or convex algorithms perform poorly under non-Gaussian heavy-tailed noise conditions or in the face of outliers. In this paper, we propose the usage of mixed $\ell_{p,q}$ norms on data fidelity (residual matrix) term and the conventional $\ell_{0,2}$-norm constraint on the signal matrix to promote row-sparsity. We devise a greedy pursuit algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Simulation studies highlight the effectiveness of the proposed approaches to cope with different noise environments (i.i.d., row i.i.d, etc) and outliers. Usefulness of the methods are illustrated in source localization application with sensor arrays.Comment: Paper appears in Proc. European Signal Processing Conference (EUSIPCO'15), Nice, France, Aug 31 -- Sep 4, 201

Transmission Eigenvalues for a Class of Non-Compactly Supported Potentials

Let $\Omega\subseteq\mathbb R^n$ be a non-empty open set for which the Sobolev embedding $H_0^2(\Omega)\longrightarrow L^2(\Omega)$ is compact, and let $V\in L^\infty(\Omega)$ be a potential taking only positive real values and satisfying the asymptotics $V(\cdot)\asymp\left\langle\cdot\right\rangle^{-\alpha}$ for some $\alpha\in\left]3,\infty\right[$. We establish the discreteness of the set of real transmission eigenvalues for both Schr\"odinger and Helmholtz scattering with these potentials

The Algol triple system spatially resolved at optical wavelengths

Interacting binaries typically have separations in the milli-arcsecond regime and hence it has been challenging to resolve them at any wavelength. However, recent advances in optical interferometry have improved our ability to discern the components in these systems and have now enabled the direct determination of physical parameters. We used the Navy Prototype Optical Interferometer to produce for the first time images resolving all three components in the well-known Algol triple system. Specifically, we have separated the tertiary component from the binary and simultaneously resolved the eclipsing binary pair, which represents the nearest and brightest eclipsing binary in the sky. We present revised orbital elements for the triple system, and we have rectified the 180-degree ambiguity in the position angle of Algol C. Our directly determined magnitude differences and masses for this triple star system are consistent with earlier light curve modeling results.Comment: Accepted to Astrophysical Journal Letters, 15 pages, 2 eps figures

The High Angular Resolution Multiplicity of Massive Stars

We present the results of a speckle interferometric survey of Galactic massive stars that complements and expands upon a similar survey made over a decade ago. The speckle observations were made with the KPNO and CTIO 4 m telescopes and USNO speckle camera, and they are sensitive to the detection of binaries in the angular separation regime between 0.03" and 5" with relatively bright companions (Delta V < 3). We report on the discovery of companions to 14 OB stars. In total we resolved companions of 41 of 385 O-stars (11%), 4 of 37 Wolf-Rayet stars (11%), and 89 of 139 B-stars (64%; an enriched visual binary sample that we selected for future orbital determinations). We made a statistical analysis of the binary frequency among the subsample that are listed in the Galactic O Star Catalog by compiling published data on other visual companions detected through adaptive optics studies and/or noted in the Washington Double Star Catalog and by collecting published information on radial velocities and spectroscopic binaries. We find that the binary frequency is much higher among O-stars in clusters and associations compared to the numbers for field and runaway O-stars, consistent with predictions for the ejection processes for runaway stars. We present a first orbit for the O-star Delta Orionis, a linear solution of the close, apparently optical, companion of the O-star Iota Orionis, and an improved orbit of the Be star Delta Scorpii. Finally, we list astrometric data for another 249 resolved and 221 unresolved targets that are lower mass stars that we observed for various other science programs.Comment: 76 pages, 6 figures, 11 table

A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I

A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the likelihood for the parameters characterizing the discrete objects by an alternative exact form that is much quicker to evaluate; ii) using a simultaneous multiple minimization code based on Powell's direction set algorithm to locate rapidly the local maxima in the posterior; and iii) deciding whether each located posterior peak corresponds to a real object by performing a Bayesian model selection using an approximate evidence value based on a local Gaussian approximation to the peak. The construction of this Gaussian approximation also provides the covariance matrix of the uncertainties in the derived parameter values for the object in question. This new approach provides a speed up in performance by a factor of `hundreds' as compared to existing Bayesian source extraction methods that use MCMC to explore the parameter space, such as that presented by Hobson & McLachlan. We illustrate the capabilities of the method by applying to some simplified toy models. Furthermore PowellSnakes has the advantage of consistently defining the threshold for acceptance/rejection based on priors which cannot be said of the frequentist methods. We present here the first implementation of this technique (Version-I). Further improvements to this implementation are currently under investigation and will be published shortly. The application of the method to realistic simulated Planck observations will be presented in a forthcoming publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted for publication in MNRA

Angular Diameters and Effective Temperatures of Twenty-five K Giant Stars from the CHARA Array

Using Georgia State University's CHARA Array interferometer, we measured angular diameters for 25 giant stars, six of which host exoplanets. The combination of these measurements and Hipparcos parallaxes produce physical linear radii for the sample. Except for two outliers, our values match angular diameters and physical radii estimated using photometric methods to within the associated errors with the advantage that our uncertainties are significantly lower. We also calculated the effective temperatures for the stars using the newly-measured diameters. Our values do not match those derived from spectroscopic observations as well, perhaps due to the inherent properties of the methods used or because of a missing source of extinction in the stellar models that would affect the spectroscopic temperatures

An asteroseismic study of the Beta Cephei star Theta Ophiuchi: photometric results

We have carried out a three-site photometric campaign for the Beta Cephei star Theta Ophiuchi from April to August 2003. 245 hours of differential photoelectric uvy photometry were obtained during 77 clear nights. The frequency analysis of our measurements resulted in the detection of seven pulsation modes within a narrow frequency interval between 7.116 and 7.973 c/d. No combination or harmonic frequencies were found. We performed a mode identification of the individual pulsations from our colour photometry that shows the presence of one radial mode, one rotationally split l=1 triplet and possibly three components of a rotationally split l=2 quintuplet. We discuss the implications of our findings and point out the similarity of the pulsation spectrum of Theta Ophiuchi to that of another Beta Cephei star, V836 Cen.Comment: 8 pages, 6 figure