Analysis of Multiband Astronomical Images using Multiscale Tools
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1 Anaysis of Mutiband Astronomica Images using Mutiscae Toos A.Bijaoui A.Guennec Ch.Benoist & E.Seza Cassioée Laboratory Côte d Azur Observatory BP Nice Cedex 04 France
2 Outines Astronomica Imaging & Virtua Observatories Mutiband / Mutiwaveength images Needs of a mutiscae anaysis Fusion Image Anaysis of fusion image Pixe casses identification Mixing & Pure eements Casses maing Source searation 24th October 2005 Waveet Aications in Industria Processing 2
3 Today Astronomica Imaging Generaization of wide-fied CCD cameras Observation on the whoe sectra range Fiters # waveength and # width Sectro-imaging deveoments Consistent surveys with a arge diffusion Pieine re-rocessing softwares Instrumenta corrections Radiometrica transformation Geometrica registration 24th October 2005 Waveet Aications in Industria Processing 3
4 The Virtua Observatory Astronomica data centers Ex. Strasbourg data center Diffused information Cataogs reduced images artices Interconnection between stored data Anaysis software From des to bases Interoerabiity Dedicated software for anayzing the information 24th October 2005 Waveet Aications in Industria Processing 4
5 Anaysis of Mutiband Astronomica Images Many accessibe reevant surveys Soan Digita Sy Survey SDSS Canada France Hawaï Legacy Survey Hubbe Sace Teescoe images Puroses Consistent detection & measurements Pixe / object cassification The EIS/GOODS fied Use of 6 bands : U U B V R & I 2000x2000 sames 24th October 2005 Waveet Aications in Industria Processing 5
6 B Image 24th October 2005 Waveet Aications in Industria Processing 6
7 U-U-B-V-R-I Images 24th October 2005 Waveet Aications in Industria Processing 7
8 Fusion Image Sufficient statistics for co-addition x n =c n x nu mean standard deviation σ n y=σ c n x n / σ n 2 is a sufficient statistics for fusion Best signa to noise ratio combination Determination of the scaar factor c n Gobay on the image Variations due to coor Pixe / Pixe Chi2-square exression Raw chi-2 image Very noisy Needs of smoothing/denoising 24th October 2005 Waveet Aications in Industria Processing 8
9 Chi-2 image from PSF Smoothing Adated smoothing with the PSF PSF = stear rofie Imrovement of the star detection Systematic use for astronomica images PSF determination Needs to seect isoated stars Sace variations Chi-2 images from PSF smoothing Variations of the PSF / image 24th October 2005 Waveet Aications in Industria Processing 9
10 Chi-2 image from Denoising Aication of a discrete waveet transformation Redundant / Unredundant agorithms À trous agorithm Reduction of the coefficient vaues with a softening function Donoho s rue From a Bayesian aroach Generaization of the Wiener fitering / Gaussian mixture Direct or reguarized inversion Direct inversion unredundant transforms Orthogona rojection for the à trous Reguarized inversion Sensitivity to the bacground subtraction 24th October 2005 Waveet Aications in Industria Processing 10
11 24th October 2005 Waveet Aications in Industria Processing 11 Chi-2 image from restoration 1 If the PSFs are nown it is ossibe to do a deconvoution on the images Aication of Richarson-Lucy s agorithm With ] [ 1 V V W W = + W V =
12 24th October 2005 Waveet Aications in Industria Processing 12 Chi-2 image from restoration 2 Residue Reation with residue Significant residue > denoising Positivity constraint Fina smoothing with the same PSF V V r = ] [ 1 V r W W W + = +
13 Restored / Smoothed Image Noise estimation robem Noise excess at the first scae Sensitivity to the bacground estimation 24th October 2005 Waveet Aications in Industria Processing 13
14 Chi-2 images 24th October 2005 Waveet Aications in Industria Processing 14
15 The best Fusion image Raw B Image Restoration & PSF smoothing 24th October 2005 Waveet Aications in Industria Processing 15
16 Detection from the Fusion Image Aication of Sextractor Mutiscae detection Mutiband measurements from radia rofies Raw Chi-2 Denoised PSF smoothing Restored & smoothed Scae Waveet Sext th October 2005 Waveet Aications in Industria Processing 16
17 Coor Anaysis Probems with the cassica coor indices Negative / nu fuxes Coor noise vs magnitude Non additivity from comonents Use of ratios / weighted mean Estimation of a ositive image Use of the restored / smoothed images Ratio noise / weighted mean Additivity from comonents 24th October 2005 Waveet Aications in Industria Processing 17
18 Raw ratios Restoration & PSF smoothing B / weighted mean ratio 24th October 2005 Waveet Aications in Industria Processing 18
19 Mased anaysis The ratio noise deends on the intensity Mas comuted from this deendency The statistica quantities are comuted from this mas 24th October 2005 Waveet Aications in Industria Processing 19
20 K-means Cassification Iteration 10 seected casses The mas is aied from the estimations Threshoding Mas>0.5 Rejection of too far ixes Not enough casses 24th October 2005 Waveet Aications in Industria Processing 20
21 Sources from Casses A cass = sectra distribution A The ixe intensities as mixing: V = AX + N X are the sources : cass roortions Knowing V & A getting X : i-osed robem number of casses > number of images Use of a CLEAN-ie agorithm 24th October 2005 Waveet Aications in Industria Processing 21
22 Resuting Sources th October 2005 Waveet Aications in Industria Processing 22
23 Concusion Toos for the Virtua Observatory Detection imroved from the Fusion image Consistent measurements from many bands Pixe cassification from ratios Waveet restorations carry out avaiabe images Pixe cassification Source searation / Casses carries out a intermediate descrition 24th October 2005 Waveet Aications in Industria Processing 23
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