We show how a wavelet-based image adaptive deconvolution algorithm can provide significant improvements in the analysis of wide-field CCD images. To illustrate it, we apply our deconvolution protocol to a set of images from a Baker-Nunn telescope. This f/1 instrument has an outstanding field of view of 4.4°x4.4° with high optical quality offering unique properties to study our deconvolution process and results. In particular, we obtain an estimated gain in limiting magnitude of ΔR∼0.6 mag and in limiting resolution of Δρ∼3.9 arcsec. These results increase the number of targets and the efficiency of the underlying scientific project

Cardinal, Robert D.

Fors Aldrich, Octavi

Hildebrand, A.R.

Merino, M.T.

Núñez de Murga, Jorge, 1955-

Otazu Porter, Xavier

Publications of the Astronomical Society of the Pacific

English

Diposit Digital de la Universitat de Barcelona

Astronomical Data Analysis Software and Systems XVASP Conference Series, Vol. 351, 2006C. Gabriel, C. Arviset, D. Ponz and E. Solano, eds.Wavelet-Based Image Deconvolution for Wide Field CCDImageryMaria Teresa Merino1, Octavi Fors12, Xavier Otazu3, Rob Cardinal4,Jorge Núñez12, A.R. Hildebrand4Abstract. We show how a wavelet-based image adaptive deconvolutionalgorithm can provide significant improvements in the analysis of wide-field CCD images. To illustrate it, we apply our deconvolution protocol toa set of images from a Baker-Nunn telescope. This f/1 instrument has anoutstanding field of view of 4.4◦x4.4◦ with high optical quality offeringunique properties to study our deconvolution process and results. Inparticular, we obtain an estimated gain in limiting magnitude of ∆R∼0.6mag and in limiting resolution of ∆ρ∼3.9′′. These results increase thenumber of targets and the efficiency of the underlying scientific project.1. IntroductionSignal processing has progressed significantly during the last decade. The devel-opment of the multiresolution concept based on wavelets and the use of adaptivedeconvolution by using signal detection masks have improved the performanceof traditional algorithms, specially in terms of noise amplification reduction, acrucial aspect in astronomical images (Starck et al. 2002).But deconvolution in Astronomy is still usually restricted to a few particularapplications where the original images have some specific ideal properties. Inundersampled or poorly sampled images, it is known that deconvolved imagesusually violate the sampling theorem (Magain 1998) introducing problems in theposterior analysis such as accurate astrometry and photometry. Moreover, incases such as wide field instruments’ data with noticeable distortions we also faceadditional complications such as variable background and variable PSF acrossthe image, problems obtaining acceptable flats, etc.The aim of this example is to show how a wavelet-based Bayesian adap-tive deconvolution algorithm can also provide important improvements to thoseprojects with data showing non-ideal features. In the following sections we de-scribe the techniques used, the data processed and how deconvolution can makesignificant improvements to achieve the underlying scientific goals.1Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Spain2Observatori Fabra, Barcelona, Spain3Centre de Visió per Computador, Universitat Autònoma de Barcelona, Spain4Rothney Astrophysical Observatory, University of Calgary, Canada153154 Merino, Fors, Otazu, Cardinal, Núñez & Hildebrand2. Baker-Nunn Data DeconvolutionWe deconvolved ten, 30s, 0.8◦x0.8◦ central subframes of the same region of thesky obtained in a not ideal night (seeing∼3′′) with FWHM∼2.1 pixels using theBaker-Nunn Telescope at the Rothney Astrophysical Observatory (Calgary).Baker-Nunn cameras were built during Cold War as 50cm f/1 photographicmodified Schmidt altazimutal instruments for satellite tracking. Rothney’s wasretrofitted to work with a 4kx4k-9µm CCD providing a field of view of 4.4◦x4.4◦with high optical quality (spot size ∼ 20µm) and 3.9′′/pixel. It is searchingfor NEOs in the North pole regions since 2003 (NESS-T project), though somecalibrations are still being held to evaluate other possible uses as variable starsstudies. Some of us are retrofitting another Baker-Nunn in Spain (Núñez et al.2003) with some differences in optical design and observational strategy. Theseinstruments show unique properties and allow very fast and efficient surveys.To increase NEOs detections it is crucial to push limiting magnitude as faintas possible. Besides, its sampling (close to be critical) results in common objectblending, so it is also important to improve the deblending and resolution ofthe detected objects. These are the main goals of deconvolving this wide fieldmarginally sampled data even though it has some additional properties not de-sired for this kind of processing (variable background and PSF, difficulties inobtaining proper flats, overblooming, ...).The deconvolution algorithm used is a modified MLE (Gauss+Poisson) usingwavelets and adaptive deconvolution. The basic primitive algorithm belongs tothe group based on a maximum likelihood estimator (MLE) derived throughBayesian methodology considering noise being Poisson and Gauss. Our im-plementation, named AWMLE, was upgraded (Otazu 2001) to incorporate themultiresolution concept working onto wavelets decomposition and the adaptivedeconvolution using probability masks. These additional features allow detectionand deconvolution of only real signal features and minimize noise amplificationand false detections.A new methodology for this application was defined (Fors 2006): (1) CCDframes calibration; (2) astrometric plate transformation of every frame Ii toI1 and then also to the reference catalog USNOA2.0 (Monet et al. 1998); (3)aperture photometry of reference stars and PSF fitting with a subset of bestcandidate stars with different PSF models hybrid (Gaussian, Moffat15 andLorentz) and purely analytical (Penny); (4) frames deconvolution with eachPSF model keeping partial results up to 200 iterations; (5) object detectionwith SExtractor (Bertin & Arnouts 1996) at 2σ and 3σ thresholds with darknature effects masked; (6) matchings between all frame-catalogs and matchingswith USNOA2.0; (7) false detections and deblending analysis at 2σ-threshold;(8) limiting magnitude gain with respect to USNOA2.0 (R-mag) at 3σ-threshold.Most steps were done with IRAF (Tody 1986), or with custom processing tools.3. ResultsPSF influence: Moffat15 delivered a larger number of matched detections (max-imum at ∼140-iter) but Lorentz reached its maximum earlier (at ∼120-iter)with significantly less false detections. Differences are from Moffat15 minimalImage Deconvolution for Wide Field CCD Imagery 155residuals in the core compared to Lorentz’s better fit to the outer wings of thePSF. Gaussian and Penny gave poorer results because are worse fitting modelsfor this data. The non-assymptotic convergence in detections vs. iterations overthe maximum is due to not having a well estimated background and flat-field.Table 1. Original, Moffat15(140-iter) and Lorentz(120-iter) 2σ-detectionsImage Raw Matched Unmatched (%)Original 1734 1724 0.4Moffat15 (140 iterations) 2733 2644 3.2Lorentz (120 iterations) 2677 2610 2.5False Detections: Table 1 shows results for one of the frames and its bestdeconvolutions. Most of the few unmatched detected objects are due to PSFmismatch and ringing (57 Moffat15, 48 Lorentz), both effects appearing be-cause of the sampling theorem violation, typical in deconvolution of marginallysampled data. Some are false detections because deconvolution of overbloomingaround bright stars, ghosts created by internal reflections (4 original, 7 Moffat15,5 Lorenz), or objects not in USNOA2.0 but included in USNOB1.0 (3 original,4 Moffat15&Lorentz). Only 16 in Moffat15 and 7 in Lorentz remain as truemarginal false detections and all them vanished in the 200-iter images. They arevery reasonable amounts considering the limited PSF modelling and the non-assymptotic convergence constraints explained above. Moreover, although notbeing real, we remark the recoveries of the 2 ghosts and the 1 missing object inUSNOA2.0 detected in the deconvolved but too faint or blended in the originalimage. They show that the algorithm could recover some possible slightly faintor blended asteroids. Unfortunately this FOV has no asteroid, but repeating thisstudy with other frames with known faint asteroids is a future work in process.Resolution Gain: Figure 1a shows near resolved objects vs. separation upto 30 pixels in the original vs. the Moffat15 deconvolved image. Some of thenew resolved objects might appear merely because of the increase of new faintdetections, but specially for those separations until a few FWHMs most of themare more likely due to the deblending. To compute an estimation of the limitingresolution gain with deconvolution we look at the minimum separation betweenobjects in the original image (3.7 pixels) and in the deconvolved one (2.7 pixels).That leads to a limiting resolution gain of 3.9′′, crucial specially for workingin crowded areas with poorly sampled instruments where there is a significantprobability of loosing asteroids due to blending with a nearby star.Magnitude Gain: To evaluate the magnitude gain we do detections with themore usually accepted 3σ threshold instead of the 2σ threshold more common formerely asteroid detection. Matching tolerance radius is 2.25 pixels since showedto be a a good compromise avoiding false matched besides false unmatcheddue to errors in catalogs, transformations and centroiding. Using USNOA2.0as reference catalog instead of others more complete or accurate ones is notvery relevant for our specific data properties to only get a relative estimate.156 Merino, Fors, Otazu, Cardinal, Núñez & HildebrandFigure 1. a) Resolution Gain b) Magnitude Gain0 5 10 15 20 25 30Separation (pixels)0255075100125Number of resolved objectsOriginalAWMLE 140 iterations Moffat15 PSFLimiting resolution of NESS−Tdeconvolved imageNESS−T original image Limiting resolution of 8 10 12 14 16 18 20USNO-A2.0 R magnitude0100200300400500# detectionsAWMLE 140 iterations Moffat15 PSFOriginal   Figure 1b illustrates matched detections vs. USNOA2.0 R-mag for the originaland Moffat15(140-iter) deconvolved frames. A dramatic recovery of faint objectsby the deconvolution application is shown. The estimate of limiting magnitudegain by simply applying the area ratio of the histograms results in ∆R∼0.6mag. Note that this ∆R gain estimate does not take into account the intrinsicmagnitude distribution in the studied FOV and so could be somewhat biased.4. ConclusionsDeconvolution can add important benefits to the use of wide field and marginallysampled Baker-Nunn data for NEO surveys, even with difficulties such as thevariable PSF and background, not proper flat, overblooming,etc. We show firstlyhow our deconvolution protocol decisively increases the detections with only afew and reasonable false ones providing a limiting magnitude gain ∆R∼0.6 magand secondly how improves near objects deblending with limiting resolution gain∆ρ∼3.9′′. Similar improvements by using deconvolution may be also useful todata from other observational facilities usually not considered to be deconvolved.Acknowledgments. M. Merino is supported by a fellowship from the MEC,Spain, Ref. AP2002-2676; X. Otazu by the program Ramon y Cajal, foundedby the MEC; A. Hildebrand by the Canada Research Chair Program.ReferencesBertin, E., & Arnouts, S. 1996, A&A, 117, 393Fors, O. 2006, Dept. Astronomia i Meteorologia, Univ. Barcelona, PhD ThesisMagain, P., Courbin, F., & Sohy, S. 1998, AJ, 494, 472Monet, D. et al. 1998, VizieR Online Data Catalog, 1252Núñez, J. et al. 2003, Proc. Jornadas Cient́ıficas 250 Años de Astronomı́a, 153Otazu, X. 2001, Dept. Astronomia i Meteorologia, Univ. Barcelona, PhD ThesisStarck et al. 2002, PASP, 114, 1051Tody, D. 1986, Proc. SPIE Instrumentation in Astronomy, 627, 733

Wavelet-based Image deconvolution for Wide Field CCD Imagery

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Wavelet-based Image deconvolution for Wide Field CCD Imagery

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