Nonparametric Edge Detection in Speckled Imagery

We address the issue of edge detection in Synthetic Aperture Radar imagery. In particular, we propose nonparametric methods for edge detection, and numerically compare them to an alternative method that has been recently proposed in the literature. Our results show that some of the proposed methods display superior results and are computationally simpler than the existing method. An application to real (not simulated) data is presented and discussed.Comment: Accepted for publication in Mathematics and Computers in Simulatio

Nonparametric Fixed-Interval Smoothing of Nonlinear Vector-Valued Measurements

The problem of estimating a smooth vector-valued function given noisy nonlinear vector-valued measurements of that function is addressed. A nonparametric optimality criterion for this estimation problem is presented, and a computationally efficient iterative algorithm for its solution is developed. The criterion is the natural generalization of previously published work on vector splines with linear measurement models. The algorithm provides an alternative to the extended Kalman filter, as it does not require a parametric state-space model. An automatic procedure that uses the measurements to determine how much to smooth is presented. The algorithm's subpixel estimation accuracy is demonstrated on the estimation of a curved edge in a noisy image and on a biomedical image-processing application.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85839/1/Fessler112.pd

Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope

The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients. We present in this paper an extension of the MSVST to 3D data (in fact 2D-1D data) when the third dimension is not a spatial dimension, but the wavelength, the energy, or the time. We show that the MSVST can be used for detecting and characterizing astrophysical sources of high-energy gamma rays, using realistic simulated observations with the Large Area Telescope (LAT). The LAT was launched in June 2008 on the Fermi Gamma-ray Space Telescope mission. The MSVST algorithm is very fast relative to traditional likelihood model fitting, and permits efficient detection across the time dimension and immediate estimation of spectral properties. Astrophysical sources of gamma rays, especially active galaxies, are typically quite variable, and our current work may lead to a reliable method to quickly characterize the flaring properties of newly-detected sources.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_msvst.pd

The Stellar Dynamics of Omega Centauri

The stellar dynamics of Omega Centauri are inferred from the radial velocities of 469 stars measured with CORAVEL (Mayor et al. 1997). Rather than fit the data to a family of models, we generate estimates of all dynamical functions nonparametrically, by direct operation on the data. The cluster is assumed to be oblate and edge-on but mass is not assumed to follow light. The mean motions are consistent with axisymmetry but the rotation is not cylindrical. The peak rotational velocity is 7.9 km/s at 11 pc from the center. The apparent rotation of Omega Centauri is attributable in part to its proper motion. We reconstruct the stellar velocity ellipsoid as a function of position, assuming isotropy in the meridional plane. We find no significant evidence for a difference between the velocity dispersions parallel and perpendicular to the meridional plane. The mass distribution inferred from the kinematics is slightly more extended than, though not strongly inconsistent with, the luminosity distribution. We also derive the two-integral distribution function f(E,Lz) implied by the velocity data.Comment: 25 Latex pages, 12 Postscript figures, uses aastex, epsf.sty. Submitted to The Astronomical Journal, December 199

Dust and the Infrared Kinematic Properties of Early-Type Galaxies

We have obtained spectra and measured the stellar kinematics in a sample of 25 nearby early-type galaxies (with velocity dispersions from less than 100 km/s to over 300 km/s) using the near-infrared CO absorption bandhead at 2.29 microns. Our median uncertainty for the dispersions is ~10%. We examine the effects of dust on existing optical kinematic measurements. We find that the near-infrared velocity dispersions are in general smaller than optical velocity dispersions, with differences as large as 30%. The median difference is 11% smaller, and the effect is of greater magnitude for higher dispersion galaxies. The lenticular galaxies (18 out of 25) appear to be causing the shift to lower dispersions while the classical ellipticals (7 out of 25) are consistent between the two wavelength regimes. If uniformly distributed dust causes these differences, we would expect to find a correlation between the relative amount of dust in a galaxy and the fractional change in dispersion, but we do not find such a correlation. We do see correlations both between velocity dispersion and CO bandhead equivalent width, and velocity dispersion and Mg2 index. The differences in dispersion are not well explained by current models of dust absorption. The lack of correlation between the relative amount of dust and shift in dispersion possibly suggets that dust does not have a similar distribution from galaxy to galaxy. The CO equivalent widths of these galaxies are quite high (>10 angstroms for almost all), requiring the light at these wavelengths to be dominated by very cool stars.Comment: 17 pages, 14 figures, accepted to The Astronomical Journa