Bayesian Analysis of Many-Pole Fits of Hadron Propagators in Lattice QCD

We use Bayes' probability theorem to analyze many-pole fits of hadron propagators. An alternative method of estimating values and uncertainties of the fit parameters is offered, which has certain advantages over the conventional methods. The probability distribution of the parameters of a fit is calculated. The relative probability of various models is calculated.Comment: 4 pages, 6 figures, Latex with espcrc2.sty, uuencoded compressed tar file contains 7 Latex files: 1 with the paper and 6 with the figures. Talk presented at LATTICE96(spectrum

Noise Variance Estimation In Signal Processing

We present a new method of estimating noise variance. The method is applicable for 1D and 2D signal processing. The essence of this method is estimation of the scatter of normally distributed data with high level of outliers. The method is applicable to data with the majority of the data points having no signal present. The method is based on the shortest half sample method. The mean of the shortest half sample (shorth) and the location of the least median of squares are among the most robust measures of the location of the mode. The length of the shortest half sample has been used as the measurement of the data scatter of uncontaminated data. We show that computing the length of several sub samples of varying sizes provides the necessary information to estimate both the scatter and the number of uncontaminated data points in a sample. We derive the system of equations to solve for the data scatter and the number of uncontaminated data points for the Gaussian distribution. The data scatter is the measure of the noise variance. The method can be extended to other distributions

Fast Direct Plane-to-Plane Coordinate Transformations

A set of highly efficient coordinate transformations has been derived to convert between Cartesian coordinates in two different projection planes. The gain in execution speed is as great as a factor of 20 compared to the two‐step process of going from Cartesian coordinates in one plane to the celestial coordinates, and then to Cartesian coordinates in the second plane. The new coordinate transformations are successfully used by the Spitzer Space Telescope mosaicker MOPEX

Spectral Density on the Lattice

Spectral density in the pseudoscalar and vector channels is extracted from the SU(2) lattice quenched data. It is shown to consist of three sharp poles within the energy range accessible on the lattice.Comment: 38 pages, uuencoded tar-compressed ps-fil

Mosaicking with MOPEX

We present MOPEX - a software package for image mosaicking and point source extraction. MOPEX has been developed for the pitzer Space Telescope. This paper concentrates on the mosaicking aspects of the package. MOPEX features the use of several interpolation techniques, coaddition schemes, and robust and flexible outlier detection based on spatial and temporal filtering. A number of original algorithms have been designed and implemented in MOPEX. Among them is direct plane-to-plane coordinate transformation, which allows at least an order of magnitude speed up in performing coordinate transformation by bypassing the sky coordinates. The dual outlier detection makes possible outlier detection in the areas of even minimal redundancy. Image segmentation based on adaptive thresholding is used for object detection, which is part of outlier detection. Efficient use of computer memory allows mosaicking of data sets of very deep coverage of thousands of images per pointing, as well as areas of sky covering many square degrees. Although designed for Spitzer data, MOPEX does not require any Spitzer-specific fits header keywords to run, and can be applied to other data, that have standard header information on the image geometry and pointing. The package is available for distribution at http://ssc.spitzer.caltech.edu/postbcd/

Point Source Extraction with MOPEX

MOPEX (MOsaicking and Point source EXtraction) is a package developed at the Spitzer Science Center for astronomical image processing. We report on the point source extraction capabilities of MOPEX. Point source extraction is implemented as a two step process: point source detection and profile fitting. Non-linear matched filtering of input images can be performed optionally to increase the signal-to-noise ratio and improve detection of faint point sources. Point Response Function (PRF) fitting of point sources produces the final point source list which includes the fluxes and improved positions of the point sources, along with other parameters characterizing the fit. Passive and active deblending allows for successful fitting of confused point sources. Aperture photometry can also be computed for every extracted point source for an unlimited number of aperture sizes. PRF is estimated directly from the input images. Implementation of efficient methods of background and noise estimation, and modified Simplex algorithm contribute to the computational efficiency of MOPEX. The package is implemented as a loosely connected set of perl scripts, where each script runs a number of modules written in C/C++. Input parameter setting is done through namelists, ASCII configuration files. We present applications of point source extraction to the mosaic images taken at 24 and 70 micron with the Multiband Imaging Photometer (MIPS) as part of the Spitzer extragalactic First Look Survey and to a Digital Sky Survey image. Completeness and reliability of point source extraction is computed using simulated data.Comment: 20 pages, 13 Postscript figures, accepted for publication in PAS

Bayesian curve fitting for lattice gauge theorists

A new method of extracting the low-lying energy spectrum from Monte Carlo estimates of Euclidean-space correlation functions which incorporates Bayesian inference is described and tested. The procedure fully exploits the information present in the correlation functions at small temporal separations and uses this information in a way consistent with fundamental probabilistic hypotheses. The computed errors on the best-fit energies include both statistical uncertainties and systematic errors associated with the treatment of contamination from higher-lying stationary states. Difficulties in performing the integrals needed to compute these error estimates are briefly discussed.Comment: 7 pages, 6 figures, 2 tables, uses espcrc2. Talk presented at the Workshop on Lattice Hadron Physics, Colonial Club Resort, Cairns, Australia, July 9-18, 200

Efficient Mosaicking of Spitzer Space Telescope Images

A parallel version of the MOPEX software, which generates mosaics of infrared astronomical images acquired by the Spitzer Space Telescope, extends the capabilities of the prior serial version. In the parallel version, both the input image space and the output mosaic space are divided among the available parallel processors. This is the only software that performs the point-source detection and the rejection of spurious imaging effects of cosmic rays required by Spitzer scientists. This software includes components that implement outlier-detection algorithms that can be fine-tuned for a particular set of image data by use of a number of adjustable parameters. This software has been used to construct a mosaic of the Spitzer Infrared Array Camera Shallow Survey, which comprises more than 17,000 exposures in four wavelength bands from 3.6 to 8 m and spans a solid angle of about 9 square degrees. When this software was executed on 32 nodes of the 1,024-processor Cosmos cluster computer at NASA s Jet Propulsion Laboratory, a speedup of 8.3 was achieved over the serial version of MOPEX. The performance is expected to improve dramatically once a true parallel file system is installed on Cosmos

Filtering of Signal Dependent Noise Applied to MIPS Data

Linear filtering and usual nonlinear median filtering are not effective for signal-dependent noise removal. We apply here an approximate decoupling of signal and noise by means of a nonlinear transform. The transform is followed by a linear filter and the corresponding inverse transform. This procedure allows us to mitigate the signal-dependent noise in the images obtained by the Multiband Imaging Photometer for Spitzer (MIPS), 70μm imaging band