Shannon sampling and nonlinear dynamics on graphs for representation, regularization and visualization of complex data

Data is now produced faster than it can be meaningfully analyzed. Many modern data sets present unprecedented analytical challenges, not merely because of their size but by their inherent complexity and information richness. Large numbers of astronomical objects now have dozens or hundreds of useful parameters describing each one. Traditional color-color plots using a limited number of symbols and some color-coding are clearly inadequate for finding all useful correlations given such large numbers of parameters. To capitalize on the opportunities provided by these data sets one needs to be able to organize, analyze and visualize them in fundamentally new ways. The identification and extraction of useful information in multiparametric, high-dimensional data sets - data mining - is greatly facilitated by finding simpler, that is, lower-dimensional abstract mathematical representations of the data sets that are more amenable to analysis. Dimensionality reduction consists of finding a lower-dimensional representation of high-dimensional data by constructing a set of basis functions that capture patterns intrinsic to a particular state space. Traditional methods of dimension reduction and pattern recognition often fail to work well when performed upon data sets as complex as those that now confront astronomy. We present here our developments of data compression, sampling, nonlinear dimensionality reduction, and clustering, which are important steps in the analysis of large-scale, complex datasets

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

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Needatool: A Needlet Analysis Tool for Cosmological Data Processing

We introduce NeedATool (Needlet Analysis Tool), a software for data analysis based on needlets, a wavelet rendition which is powerful for the analysis of fields defined on a sphere. Needlets have been applied successfully to the treatment of astrophysical and cosmological observations, and in particular to the analysis of cosmic microwave background (CMB) data. Usually, such analyses are performed in real space as well as in its dual domain, the harmonic one. Both spaces have advantages and disadvantages: for example, in pixel space it is easier to deal with partial sky coverage and experimental noise; in harmonic domain, beam treatment and comparison with theoretical predictions are more effective. During the last decade, however, wavelets have emerged as a useful tool for CMB data analysis, since they allow to combine most of the advantages of the two spaces, one of the main reasons being their sharp localisation. In this paper, we outline the analytical properties of needlets and discuss the main features of the numerical code, which should be a valuable addition to the CMB analyst's toolbox.Comment: software available at: http://www.fisica.uniroma2.it/~pietrobon/dp_files/dp_NeedATool_download.htm

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

On Orbit Performance of the MIPS Instrument

The Multiband Imaging Photometer for Spitzer (MIPS) provides long wavelength capability for the mission, in imaging bands at 24, 70, and 160 microns and measurements of spectral energy distributions between 52 and 100 microns at a spectral resolution of about 7%. By using true detector arrays in each band, it provides both critical sampling of the Spitzer point spread function and relatively large imaging fields of view, allowing for substantial advances in sensitivity, angular resolution, and efficiency of areal coverage compared with previous space far-infrared capabilities. The Si:As BIB 24 micron array has excellent photometric properties, and measurements with rms relative errors of 1% or better can be obtained. The two longer wavelength arrays use Ge:Ga detectors with poor photometric stability. However, the use of 1.) a scan mirror to modulate the signals rapidly on these arrays, 2.) a system of on-board stimulators used for a relative calibration approximately every two minutes, and 3.) specialized reduction software result in good photometry with these arrays also, with rms relative errors of less than 10%

Spitzer 70 and 160-micron Observations of the Extragalactic First Look Survey

We present Spitzer 70um and 160um observations of the Spitzer extragalactic First Look Survey (xFLS). The data reduction techniques and the methods for producing co-added mosaics and source catalogs are discussed. Currently, 26% of the 70um sample and 49% of the 160um-selected sources have redshifts. The majority of sources with redshifts are star-forming galaxies at z<0.5, while about 5% have infrared colors consistent with AGN. The observed infrared colors agree with the spectral energy distribution (SEDs) of local galaxies previously determined from IRAS and ISO data. The average 160um/70um color temperature for the dust is Td~= 30+/-5 K, and the average 70um/24um spectral index is alpha~= 2.4+/-0.4. The observed infrared to radio correlation varies with redshift as expected out to z~1 based on the SEDs of local galaxies. The xFLS number counts at 70um and 160um are consistent within uncertainties with the models of galaxy evolution, but there are indications that the current models may require slight modifications. Deeper 70um observations are needed to constrain the models, and redshifts for the faint sources are required to measure the evolution of the infrared luminosity function.Comment: 16 pages including 11 figures. Accepted A

On Orbit Performance of the MIPS Instrument

The Multiband Imaging Photometer for Spitzer (MIPS) provides long wavelength capability for the mission, in imaging bands at 24, 70, and 160 microns and measurements of spectral energy distributions between 52 and 100 microns at a spectral resolution of about 7%. By using true detector arrays in each band, it provides both critical sampling of the Spitzer point spread function and relatively large imaging fields of view, allowing for substantial advances in sensitivity, angular resolution, and efficiency of areal coverage compared with previous space far-infrared capabilities. The Si:As BIB 24 micron array has excellent photometric properties, and measurements with rms relative errors of 1% or better can be obtained. The two longer wavelength arrays use Ge:Ga detectors with poor photometric stability. However, the use of 1.) a scan mirror to modulate the signals rapidly on these arrays, 2.) a system of on-board stimulators used for a relative calibration approximately every two minutes, and 3.) specialized reduction software result in good photometry with these arrays also, with rms relative errors of less than 10%

Technology for a Mid-IR Flagship Mission to Characterize Earth-like Exoplanets

The exploration of Earth-like exoplanets will be enabled at mid-infrared wavelengths through technology and engineering advances in nulling interferometry and precision formation flying. Nulling interferometry provides the dynamic range needed for the detection of biomarkers. Formation flying provides the angular resolution required in the mid-infrared to separately distinguish the spectra of planets in multi-planet systems. The flight performance requirements for nulling have been met and must now be validated in a flight-like environment. Formation-flying algorithms have been demonstrated in the lab and must now be validated in space. Our proposed technology program is described