Darth Fader: Using wavelets to obtain accurate redshifts of spectra at very low signal-to-noise

We present the DARTH FADER algorithm, a new wavelet-based method for estimating redshifts of galaxy spectra in spectral surveys that is particularly adept in the very low SNR regime. We use a standard cross-correlation method to estimate the redshifts of galaxies, using a template set built using a PCA analysis on a set of simulated, noise-free spectra. Darth Fader employs wavelet filtering to both estimate the continuum & to extract prominent line features in each galaxy spectrum. A simple selection criterion based on the number of features present in the spectrum is then used to clean the catalogue: galaxies with fewer than six total features are removed as we are unlikely to obtain a reliable redshift estimate. Applying our wavelet-based cleaning algorithm to a simulated testing set, we successfully build a clean catalogue including extremely low signal-to-noise data (SNR=2.0), for which we are able to obtain a 5.1% catastrophic failure rate in the redshift estimates (compared with 34.5% prior to cleaning). We also show that for a catalogue with uniformly mixed SNRs between 1.0 & 20.0, with realistic pixel-dependent noise, it is possible to obtain redshifts with a catastrophic failure rate of 3.3% after cleaning (as compared to 22.7% before cleaning). Whilst we do not test this algorithm exhaustively on real data, we present a proof of concept of the applicability of this method to real data, showing that the wavelet filtering techniques perform well when applied to some typical spectra from the SDSS archive. The Darth Fader algorithm provides a robust method for extracting spectral features from very noisy spectra. The resulting clean catalogue gives an extremely low rate of catastrophic failures, even when the spectra have a very low SNR. For very large sky surveys, this technique may offer a significant boost in the number of faint galaxies with accurately determined redshifts.Comment: 22 pages, 15 figures. Accepted for publication in Astronomy & Astrophysic

Very high quality image restoration by combining wavelets and curvelets

We outline digital implementations of two newly developed multiscale representation systems, namely, the ridgelet and curvelet transforms. We apply these digital transforms to the problem of restoring an image from noisy data and compare our results with those obtained via well established methods based on the thresholding of wavelet coefficients. We develop a methodology to combine wavelets together these new systems to perform noise removal by exploiting all these systems simultaneously. The results of the combined reconstruction exhibits clear advantages over any individual system alone. For example, the residual error contains essentially no visually intelligible structure: no structure is lost in the reconstruction

Spherical Needlets for CMB Data Analysis

We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlets coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of these properties, we believe needlets may turn out to be especially useful in the analysis of Cosmic Microwave Background (CMB) data on the incomplete sky, as well as of other cosmological observations. As a final advantage, we stress that the implementation of needlets is computationally very convenient and may rely completely on standard data analysis packages such as HEALPix.Comment: 7 pages, 7 figure

Spectral evolution and polarization of variable structures in the pulsar wind nebula of PSR B0540-69.3

We present high spatial resolution optical imaging and polarization observations of the PSR B0540-69.3 and its highly dynamical pulsar wind nebula (PWN) performed with HST, and compare them with X-ray data obtained with the Chandra X-ray Observatory. We have studied the bright region southwest of the pulsar where a bright "blob" is seen in 1999. We show that it may be a result of local energy deposition around 1999, and that the emission from this then faded away. Polarization data from 2007 show that the polarization properties show dramatic spatial variations at the 1999 blob position arguing for a local process. Several other positions along the pulsar-"blob" orientation show similar changes in polarization, indicating previous recent local energy depositions. In X-rays, the spectrum steepens away from the "blob" position, faster orthogonal to the pulsar-"blob" direction than along this axis of orientation. This could indicate that the pulsar-"blob" orientation is an axis along where energy in the PWN is mainly injected, and that this is then mediated to the filaments in the PWN by shocks. We highlight this by constructing an [S II]-to-[O III]-ratio map. We argue, through modeling, that the high [S II]/[O III] ratio is not due to time-dependent photoionization caused by possible rapid Xray emission variations in the "blob" region. We have also created a multiwavelength energy spectrum for the "blob" position showing that one can, to within 2sigma, connect the optical and X-ray emission by a single power law. We obtain best power-law fits for the X-ray spectrum if we include "extra" oxygen, in addition to the oxygen column density in the interstellar gas of the Large Magellanic Cloud and the Milky Way. This oxygen is most naturally explained by the oxygen-rich ejecta of the supernova remnant. The oxygen needed likely places the progenitor mass in the 20 - 25 Msun range.Comment: Accepted by MNRAS on December 6th 2010, 18 pages, 15 figures. The article with full resolution figures is available here ftp://ftp.astro.su.se/pub/peter/papers/pwn0540_2010_corrected.pd

The application of a Trous wave filtering and Monte Carlo analysis on SECIS 2001 solar eclipse observations

8000 images of the Solar corona were captured during the June 2001 total Solar eclipse. New software for the alignment of the images and an automated technique for detecting intensity oscillations using multi scale wavelet analysis were developed. Large areas of the images covered by the Moon and the upper corona were scanned for oscillations and the statistical properties of the atmospheric effects were determined. The a Trous wavelet transform was used for noise reduction and Monte Carlo analysis as a significance test of the detections. The effectiveness of those techniques is discussed in detail.Comment: 17 pages, 8 figures, accepted by Solar Physics Journal for publication in Topical Issue: "Frontiers in Solar Image Processing

Dust in an extremely metal-poor galaxy: mid-infrared observations of SBS 0335-052

The metal deficient (Z = Z_sun/41) Blue Compact Dwarf Galaxy (BCD) SBS 0335-052 was observed with ISOCAM between 5 and 17 mic. With a L_12mic/L_B ratio of 2.15, the galaxy is unexpectedly bright in the mid-infrared for such a low-metallicity object. The mid-infrared spectrum shows no sign of the Unidentified Infrared Bands, which we interpret as an effect of the destruction of their carriers by the very high UV energy density in SBS 0335-052. The spectral energy distribution (SED) is dominated by a very strong continuum which makes the ionic lines of [SIV] and [NeIII] very weak. From 5 to 17 mic, the SED can be fitted with a grey-body spectrum, modified by an extinction law similar to that observed toward the Galactic Center, with an optical depth of A_V~19-21 mag. Such a large optical depth implies that a large fraction (as much as ~ 75%) of the current star-formation activity in SBS 0335-052 is hidden by dust with a mass between 3x10^3 M_sun and 5x10^5 M_sun. Silicate grains are present as silicate extinction bands at 9.7 and 18 mic can account for the unusual shape of the MIR spectrum of SBS 0335-052. It is remarkable that such a nearly primordial environment contains as much dust as galaxies which are 10 times more metal-rich. If the hidden star formation in SBS 0335-052 is typical of young galaxies at high redshifts, then the cosmic star formation rate derived from UV/optical fluxes would be underestimated.Comment: 13 pages, 4 figures, requires aaspp4.sty, accepted in Ap