Fractional Fourier detection of L\'evy Flights: application to Hamiltonian chaotic trajectories

A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited for signals having chaotic variations and sporadically appearing regular linear patterns, possibly impaired by noise. We use time-frequency techniques and the Fractional Fourier transform in order to make it robust and easily implementable. The method is illustrated with an example of application: the analysis of chaotic trajectories of advected passive particles. The signal has a chaotic behavior and encounter L\'evy flights (straight lines). The method is able to detect and quantify these ballistic transport regions, even in noisy situations

Radio Polarimetry of the ELAIS N1 Field: Polarized Compact Sources

We present deep polarimetric observations at 1420 MHz of the European Large Area ISO Survey North 1 region (ELAIS N1) as part of the Dominion Radio Astrophysical Observatory Planck Deep Fields project. By combining closely spaced aperture synthesis fields, we image a region of 7.43 square degrees to a maximum sensitivity in Stokes Q and U of 78 microJy/beam, and detect 786 compact sources in Stokes I. Of these, 83 exhibit polarized emission. We find that the differential source counts (log N - log p) for polarized sources are nearly constant down to p > 500 microJy, and that these faint polarized radio sources are more highly polarized than the strong source population. The median fractional polarization is (4.8 +/- 0.7)% for polarized sources with Stokes I flux density between 1 and 30 mJy; approximately three times larger than sources with I > 100 mJy. The majority of the polarized sources have been identified with galaxies in the Spitzer Wide Area Infrared Extragalactic Survey (SWIRE) image of ELAIS N1. Most of the galaxies occupy regions in the IRAC 5.8/3.6 micron vs. 8.0/4.5 micron color-color diagram associated with dusty AGNs, or with ellipticals with an aging stellar population. A few host galaxies have colors that suggests significant PAH emission in the near-infrared. A small fraction, 12%, of the polarized sources are not detected in the SWIRE data. None of the polarized sources in our sample appears to be associated with an actively star-forming galaxy.Comment: 28 pages, 8 Figures. Figures 2 and 3 as separate gif images. Accepted for publication in the Astrophysical Journa

Principled Design and Implementation of Steerable Detectors

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown position and orientation. We propose a continuous-domain additive image model, where the analyzed image is the sum of the template and an isotropic background signal with self-similar isotropic power-spectrum. The method is able to learn an optimal steerable filter fulfilling the SNR criterion based on one single template and background pair, that therefore strongly responds to the template, while optimally decoupling from the background model. The proposed filter then allows for a fast detection process, with the unknown orientation estimation through the use of steerability properties. In practice, the implementation requires to discretize the continuous-domain formulation on polar grids, which is performed using radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments