Morphology of the Galaxy Distribution from Wavelet Denoising

We have developed a method based on wavelets to obtain the true underlying smooth density from a point distribution. The goal has been to reconstruct the density field in an optimal way, ensuring that the morphology of the reconstructed field reflects the true underlying morphology of the point field, which, as the galaxy distribution, has a genuinely multiscale structure, with near-singular behavior on sheets, filaments, and hot spots. If the discrete distributions are smoothed using Gaussian filters, the morphological properties tend to be closer to those expected for a Gaussian field. The use of wavelet denoising provides us with a unique and more accurate morphological description.

[1]  K. Bolejko.  Evolution of cosmic structures in different environments , 2006 .

[2]  Fionn Murtagh,et al.  Astronomical Image and Data Analysis, Second Edition , 2006, Astronomy and Astrophysics Library.

[3]  D. Donoho,et al.  Analysis of the Spatial Distribution of Galaxies by Multiscale Methods , 2004, EURASIP J. Adv. Signal Process..

[4]  G. Nason,et al.  A Haar-Fisz Algorithm for Poisson Intensity Estimation , 2004 .

[5]  Albert Bijaoui,et al.  DeQuant: a flexible multiresolution restoration framework , 2004, Signal Process..

[6]  L. Hall,et al.  Acceleressence: Dark energy from a phase transition at the seesaw scale , 2004, astro-ph/0405596.

[7]  D. Madgwick,et al.  The 2dF Galaxy Redshift Survey: the clustering of galaxy groups , 2004, astro-ph/0402577.

[8]  D. Madgwick,et al.  The 2dF Galaxy Redshift Survey : higher-order galaxy correlation functions , 2004, astro-ph/0401434.

[9]  D. Madgwick,et al.  The 2dF Galaxy Redshift Survey: Voids and hierarchical scaling models , 2004, astro-ph/0401406.

[10]  D. Madgwick,et al.  The 2dF Galaxy Redshift Survey: hierarchical galaxy clustering , 2004, astro-ph/0401405.

[11]  J. Surdej,et al.  The XMM-LSS survey. First high redshift galaxy clusters: Relaxed and collapsing systems , 2003, astro-ph/0305192.

[12]  R. Ellis,et al.  The 2dF Galaxy Redshift Survey: correlation functions, peculiar velocities and the matter density of the Universe , 2002, astro-ph/0212375.

[13]  B. Sathyaprakash,et al.  Measuring the geometry and topology of large‐scale structure using SURFGEN: methodology and preliminary results , 2002, astro-ph/0210136.

[14]  Jean-Luc Starck,et al.  Astronomical image and data analysis , 2002 .

[15]  D. York,et al.  Two-dimensional Topology of the Sloan Digital Sky Survey , 2002, astro-ph/0206146.

[16]  D. Madgwick,et al.  The 2dF Galaxy Redshift Survey: The bJ-band galaxy luminosity function and survey selection function , 2001, astro-ph/0111011.

[17]  Enn Saar,et al.  Statistics of the Galaxy Distribution , 2001 .

[18]  A. Antoniadis,et al.  Wavelet shrinkage for natural exponential families with quadratic variance functions , 2001 .

[19]  I. Valtchanov,et al.  Comparison of source detection procedures for XMM-Newton images , 2001, astro-ph/0102297.

[20]  E. Kolaczyk,et al.  Nonparametric Estimation of Intensity Maps Using Haar Wavelets and Poisson Noise Characteristics , 2000 .

[21]  Robert D. Nowak,et al.  Wavelet-domain filtering for photon imaging systems , 1999, IEEE Trans. Image Process..

[22]  Robert D. Nowak,et al.  Multiscale Modeling and Estimation of Poisson Processes with Application to Photon-Limited Imaging , 1999, IEEE Trans. Inf. Theory.

[23]  Fionn Murtagh,et al.  Image Processing and Data Analysis - The Multiscale Approach , 1998 .

[24]  D. Weinberg,et al.  Mock 2dF and SDSS galaxy redshift surveys , 1998, astro-ph/9801250.

[25]  Jean-Luc Starck,et al.  Structure Detection in Low Intensity X-Ray Images using the Wavelet Transfor M Applied to Galaxy Cluster Cores Analysis , 1997, astro-ph/9707305.

[26]  T. Buchert,et al.  Beyond Genus Statistics: A Unifying Approach to the Morphology of Cosmic Structure , 1997, astro-ph/9702130.

[27]  S. Borgani,et al.  Minkowski functionals of Abell/ACO clusters , 1997 .

[28]  P. Coles,et al.  Quantifying the topology of large-scale structure , 1996, astro-ph/9603139.

[29]  Fionn Murtagh,et al.  Multiresolution Support Applied to Image Filtering and Restoration , 1995, CVGIP Graph. Model. Image Process..

[30]  Peter Coles,et al.  Cosmology: The Origin and Evolution of Cosmic Structure , 1995 .

[31]  A. Bijaoui,et al.  Objective Detection of Voids and High-Density Structures in the First CfA Redshift Survey Slice , 1993 .

[32]  Enn Saar,et al.  Wavelet analysis of the multifractal character of the galaxy distribution , 1993 .

[33]  H. Tomita.  STATISTICS AND GEOMETRY OF RANDOM INTERFACE SYSTEMS , 1990 .

[34]  D. Donoho.  One-sided inference about functionals of a density , 1988 .

[35]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[36]  D. Weinberg,et al.  The topology of the large-scale structure of the universe , 1986 .

[37]  J. Gott,et al.  The Sponge-like Topology of Large-Scale Structure in the Universe , 1986 .

[38]  R. Adler,et al.  The Geometry of Random Fields , 1982 .

[39]  H. Minkowski.  Volumen und Oberfläche , 1903 .