SoFiA: a flexible source finder for 3D spectral line data

1.3 MB·English

by  Paolo Serra

Mon.Not.R.Astron.Soc.000,1–9(2013) Printed19January2015 (MNLATEXstylefilev2.2)
SoFiA: a flexible source finder for 3D spectral line data
Paolo Serra,1(cid:63) Tobias Westmeier,2 Nadine Giese,3 Russell Jurek,1 Lars Flo¨er,4 At-
tila Popping,2,5 Benjamin Winkel,6 Thijs van der Hulst,3 Martin Meyer,2 Ba¨rbel S.
Koribalski,1 Lister Staveley-Smith2,5 and He´le`ne Courtois7
1CSIROAstronomyandSpaceScience,AustraliaTelescopeNationalFacility,POBox76,Epping,NSW1710,Australia
2ICRAR,M468,TheUniversityofWesternAustralia,35StirlingHighway,Crawley,WA6009,Australia
3UniversityofGroningen,KapteynAstronomicalInstitute,Landleven12,NL-9747AD,Groningen,theNetherlands
5 4Argelander-Institutfu¨rAstronomie,AufdemHu¨gel71,53121Bonn,Germany
1 5ARCCentreofExcellenceforAll-skyAstrophysics(CAASTRO)
0 6Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,53121Bonn,Germany
2 7Universite´Lyon1,CNRS/IN2P3,InstitutdePhysiqueNucle´aire,Lyon,France

n
a
J
Accepted2014December30.Received2014December22;inoriginalform2014July28
6
1

ABSTRACT
]
M We introduce SoFiA, a flexible software application for the detection and parameterization
ofsourcesin3Dspectral-linedatasets.SoFiAcombinesforthefirsttimeinasinglepieceof
I softwareasetofnewsource-findingandparameterizationalgorithmsdevelopedonthewayto
.
h futureHIsurveyswithASKAP(WALLABY,DINGO)andAPERTIF.Itisdesignedtoenable
p thegeneraluseofthesenewalgorithmsbythecommunityonabroadrangeofdatasets.The
- keyadvantagesofSoFiAaretheabilityto:searchforlineemissiononmultiplescalestode-
o
r tect3Dsourcesinacompleteandreliableway,takingintoaccountnoiselevelvariationsand
t thepresenceofartefactsinadatacube;estimatethereliabilityofindividualdetections;look
s
a forsignalinarbitrarilylargedatacubesusingacatalogueof3Dcoordinatesasaprior;provide
[ awiderangeofsourceparametersandoutputproductswhichfacilitatefurtheranalysisbythe

user.WehighlightthemodularityofSoFiA,whichmakesitaflexiblepackageallowingusers
1
toselectandapplyonlythealgorithmsusefulfortheirdataandsciencequestions.Thismod-
v
6 ularitymakesitalsopossibletoeasilyexpandSoFiAinordertoincludeadditionalmethods
0 astheybecomeavailable.ThefullSoFiAdistribution,includingadedicatedgraphicaluser
9 interface,ispubliclyavailablefordownload.
3
0 Keywords: methods:dataanalysis.
.
1
0
5
1 1 INTRODUCTION studied. We illustrate this point in Fig. 1, where we show a data
v: Thedetectionofastronomicalsignalaboveinstrumentalnoiseisa cubeoftheATLAS3D HIsurvey(Serraetal.2012).Inthisfigure,
i the central object is bright (and therefore easy to detect) but has
X crucial aspect of all astronomy observations. The techniques em-
acomplex3Dstructure,includingalowsurfacebrightnessexten-
ployedtodetectandcharacterisethissignaldependonthetypeof
r siontowardslargeRA.Onthecontrary,thetopobjectisbrightand
a databeinganalysed(seeMasiasetal.2012forareview).Standard
relatively simple as emission is confined within a small range of
methodsandtoolshaveemergedinfieldswithalargecommunity
RAandDec.Finally,thebottomobjectisthetypicalcaseofare-
basesuchas2Dimaging(e.g.,SExtractor;Bertin&Arnouts
solved,edge-ongalaxywherethetwopeaksofthedouble-hornve-
1996)and1Dspectroscopy(e.g.,GANDALF;Sarzietal.2006).In
locityprofileareclearlyvisible,anddetectionofthefaintemission
other fieldswith relatively fewer users,detection algorithms vary
between the two peaks is challenging. An ideal 3D source finder
significantlybetweenprojects.Thisisthecaseforstudiesbasedon
shouldbeabletodetectandparameterizeallthesedifferentsources
3D spectral line data (for brevity, data cubes), where the flux of
inacompleteandreliableway.
aspectrallineismappedasafunctionofpositionontheskyand
line-of-sightvelocityoftheemittingmatter. Radio single dishes and interferometers have traditionally
The diversity of source finding methods for data cubes is at beenthemostcommontelescopesusedtoconstructdatacubes(al-
leastpartlyduetothediversityof3Dstructureofthesourcesbeing thoughopticalintegral-fieldspectrographsarenowalsogenerating
largenumbersofsuchcubes–e.g.,Cappellarietal.2011;Croom
etal.2012;Sa´nchezetal.2012).Theupgradeandcontinuingoper-
(cid:63) E-mail:[email protected] ation of existing radio telescopes, as well as the construction of
(cid:13)c 2013RAS
2 PaoloSerraetal.
Input
data
cube
Select
sub-cube
Flagbad
voxels
Input
Apply
weights
weights
cube
S
R
E Noisenor-
LT Convolution 2D-1D malisation
FI
Figure1.Volumerenderingofan HI datacubeshowingthatindividual
sourceshaveacomplexanddiverse3Dstructure.Thismakestheirdetection
andaccurateparameterizationchallenging. RCEERS Threshold CNHI
OUND finder S+Cfinder finder
SFI
the Square Kilometre Array and its precursors, are leading to a
rapidincreaseinthenumberandsizeofdatacubes.Standardand
sufficientlygeneralsource-findingtoolswillbenecessarytoanal-
Merge Input
yse these data, and recent work has started addressing this need detected mask
(see,e.g.,DuchampbyWhiting2012).Inthispaperweintroduce voxels cube
SoFiA,anew,flexibleSourceFindingApplicationfordatacubes
whichcombinesdetectionalgorithmsandtechniquesfromseveral
sourcefinders. Rejectfalse
detections
SoFiA is designed to work on any data cube independent
of telescope or observed spectral line. However, its development
is part of preparatory work for a few specific, upcoming HI sur- Optimize
veys: WALLABY, a blind HI survey of 3/4 of the entire sky out mask
toz∼0.25tobecarriedoutwiththeAustralianSquareKilometre
ArrayPathfinder(ASKAP;seeKoribalski2012a);DINGO,adeep
HIsurveyouttoz ∼ 0.4(alsotobecarriedoutwithASKAP;see Parame-
terize
Meyer2009);andtheHIsurveysplannedforAPERTIF(Verheijen
etal.2008).Thispreparatoryworkhasresultedinthedevelopment
ofanumberofnewsource-findingalgorithms,whicharedescribed
Filter
inaseriesofpapersreferredtointhenextSection(forasummary output
seeKoribalski2012b).SoFiAputsthesedifferentalgorithmsto-
getherforthefirsttimeinacoherent,flexibleandpubliclyavailable
pieceofsoftware.
SoFiA can be obtained from https://github.com/
SoFiA-Admin/SoFiA.Onthesamewebpageweprovidealist Source Output Moment Single-
mask source
of requirements, installation instructions and a user manual. The catalogue cube maps products
aimofthispaperistodescribehowSoFiAoperatesondatacubes
andtherebyprovideareferenceforcurrentandfutureusers. Figure2.SoFiAflowchart.Wehighlightthe“Filteroutput”modulewith
adashedboxasthiswillbecomeavailableinfuturereleasesofSoFiA.
2 DESCRIPTIONOFSoFiA cube(orasub-cubeselectedbytheuser)isloaded,thesemodules
allowusersto:
SoFiAisamodularapplicationwhoseaimistodetectandparam-
eterize sources in a data cube. The flowchart in Fig. 2 shows the • modifytheinputcubebyapplyingflags,weights,orasetof
variousmodulesthatuserscanchoosetouse(ornottouse),inthe filters;
order in which they are executed by SoFiA. Once an input data • detectthespectrallinesignal;
(cid:13)c 2013RAS,MNRAS000,1–9
SoFiA3Dsourcefinder 3
switchedoff.Alternatively,itcouldbegivenanumberofrelatively
morecomplextaskssuchas,forexample,applyingawaveletfil-
teringalgorithm,rejectingfalsedetectionsorfittingmodelstothe
spectrumofthedetectedsources.
WhileSoFiAwillcontinuetobeimproved,thisbasicprinci-
pleofmodularitywillnotchange.Therefore,althoughthispaper
describes the software as it is at the time of writing and new al-
gorithms may be introduced in the future, the main workings of
SoFiAwillremainasillustratedhere.
2.1 Datacube,weightscube,maskcubesandfilters
Four different types of input and/or output cubes are relevant at
differentstagesofSoFiA.
• Datacube,whichincludessignalfromastronomicalsources
superimposedoninstrumentalnoise(anderrors).
• Weights cube, which allows users to weight voxel values to
takeintoaccount,e.g.,noiselevelvariationsacrossthecubeorthe
presenceofimagingartefactsincertainregionsofthedatacube.
• Binary mask, where detected and non-detected voxels have
valuesof1and0,respectively.
• Objectmask,wherenon-detectedvoxelshaveavalueof0and
Figure3.ScreenshotoftheSoFiAGUI.TheGUIadoptsautomatically detected voxels have an integer value corresponding to the ID of
thenativestyleofthewindowmanagerusedonthesystemwhereSoFiA
theobjecttheybelongto.
isinstalled.InthisfigureweshowtheGUIasitappearsonaKubuntuLinux
system.TheGUIalsoofferstheoptionofdisplayingthesourcecatalogue Allsource-findingalgorithmsimplementedinSoFiAandde-
generatedbySoFiAandincludesahelpbrowserthatexplainstheavailable scribed in Sec. 2.2 below assume that the noise level is uniform
parametersettings. across the data cube. Therefore, noise variations caused by, e.g.,
mosaicking or frequency-dependent flagging need to be removed
first.ThiscanbedonewithinSoFiAbymeansofaweightscube
• identifysourcesbymergingdetectedvoxelstogether;
inversely proportional to the noise level. SoFiA removes noise
• rejectfalsedetections;
variationsbymultiplyingthedatacubebytheweightscube.Once
• optimizethemaskofindividualsources;
sourcedetectioniscompleted,SoFiAwillundothisoperationbe-
• measuresourceparameters;
foremeasuringsourceparameters.Theweightscubecouldalsobe
• filtertheoutputbyselectingaregionofinterestinsourcepa-
usefultodown-weightregionsofadatacubeaffectedbyimaging
rameterspace;
artefacts(e.g.,cleaningorcontinuum-subtractionresiduals).
• and produce output catalogues as well as cubes, moment
Theweightscubecanbeprovidedbytheuser.Alternatively,
maps,position-velocitydiagramsandintegratedspectra.
userscanprovideananalyticdescriptionoftheweightsvariation
Individualmodulesaredescribedinmoredetailintherestofthis across thecube. Finally, a weightscube inversely proportional to
Section. They are written in either Python or C++ and rely on a thelocalnoiselevelcanbederivedbySoFiAandappliedtothe
rangeofexternallibraries,includingNumPyandSciPy(Jonesetal. datacube.Theevaluationofthelocalnoiseleveliscarriedoutin-
2001; Walt, Colbert & Varoquaux 2011), Cython (Behnel et al. dependently along any or all of the three axes of the data cube.
2011),Astropy(AstropyCollaborationetal.2013),theGNUSci- Forexample,ausermaywishtoremovenoisevariationsalongthe
entificLibrary1and,optionally,matplotlib(Hunter2007).Provided frequencyaxisalone,undertheassumptionthatthenoisedoesnot
thattheselibrariesareavailable,SoFiAcanrunonallmachines varywithineachfrequencyplane.
withaUnixorLinuxoperatingsystem(including,e.g.,MacOSX WenotethatSoFiAmeasuresthenoisewithinadatacubeat
and Ubuntu). We refer to the SoFiA webpage for up-to-date de- variousotherstagesoftheprocessing.Differentmethodsofnoise
tails. measurementareimplementedanduserscandecidewhichoneis
SoFiA can be executed from the command line or using a moreappropriatefortheirpurpose.Possiblechoicesare:i)standard
dedicated graphical user interface (GUI) based on the Qt library deviation;ii)medianabsolutedeviation;andiii)standarddeviation
(seeFig.3).Bothmethodsallowuserstoselectwhichcombination ofazero-centredGaussianfittothenegativesideofthefluxhis-
oftheabovemodulesandwhichsourcefindingandparameteriza- togram.
tionalgorithmstouse.ThisselectionisdoneusingeithertheGUI The calculation and application of the inverse-noise weights
or a plain text parameter file (if running SoFiA from the com- cube described above is part of a more general SoFiA module
mandline),allowingthesource-findingstrategyanditscomplexity which allows users to apply a filter to the data cube before run-
to be optimized for the type of data and sources of interest. For ningtheselectedsource-findingandparameterizationalgorithms.
example, SoFiA could be asked the simple question of creating AsindicatedinFig.2,thismoduleincludestwoadditionalfiltering
amoment-0imageofallvoxelsaboveagiventhresholdinadata methods:firstly,theconvolutionwitha3Dkernelwhoseshapecan
cube – in which case most of SoFiA’s functionalities would be be chosen among a few options and whose size can be specified
bytheuser;andsecondly,the2D-1Dwaveletde-noisingalgorithm
developedbyFlo¨er&Winkel(2012).Thisalgorithmprocessesthe
1 http://www.gnu.org/software/gsl/ twospatialdimensionsandthespectraldimensionofthedatacube
(cid:13)c 2013RAS,MNRAS000,1–9
4 PaoloSerraetal.
separately,andreturnsanoise-freedatacubereconstructedusing todeliverhighercompletenessandreliabilitythanS+CandCNHI
only wavelet coefficients above a specified threshold. Additional forsourcesunresolvedonthesky,especiallyatnarrowlinewidths.
filteringoptionsmaybeprovidedinfuturereleases. Incontrast,theS+Cmethodisbyconstructionwellsuitedtofind-
AsindicatedbytheflowchartinFig.2,portionsofthecube ingsourcesonavarietyofscalesandPoppingetal.(2012)deemit
canbeblankedout(flagged)priortosourcefinding.Thismaybe thebestchoiceforextendedobjects.
necessaryatthelocationofverybrightcontinuumsourceswhose Wenotethatmanyofthealgorithmshavebeenimprovedsince
spectrumwasnotsubtractedproperlyfromthedata,oratchannels thecomparativestudyofPoppingetal.(2012).Additionaltesting
dominatedbylineemissionfromtheGalaxyoraffectedbystrong cannowbecarriedoutwithinSoFiAandwillbeusedtoinvesti-
radiofrequencyinterference. gatehowtofurtherimprovetheirperformance.Untilthen,werefer
Finally, mask cubes are generally calculated within SoFiA to the aforementioned papers for a complete discussion of these
(seebelow)butcanalsobeprovidedbytheuser.Thelattercould methods.
bedesirableifauser,followinganinitialsource-findingrun,wishes Alltheabovealgorithmsreturnabinarymaskofdetectedvox-
tolookforadditionalsourceswithadifferentsearchalgorithmor els(andanyadditionalsource-findingalgorithmcouldbeaddedto
parameters. In this case the new sources are added to the initial, SoFiAaslongastheysatisfythiscondition).Asanexample,the
inputmask.Alternatively,aninputmaskcouldbeusedifsources toppanelsofFig.4showfivechannelsextractedfromthedatacube
havealreadybeenidentifiedandonlysubsequentparameterization inFig.1and,withblackcontours,theregionsincludedinthebinary
stepsarerequired. mask.InthiscasetheS+Cfinderwasemployedusing12different
smoothingkernels.Therelativelylowadoptedthreshold(3.5σ)re-
sultsinanumberofnoisepeaksbeingincludedinthemask.We
2.2 Detectionofspectrallinesignal
comebacktothispointinSec.2.4.
SoFiA is meant to offer a number of detection algorithms that
userscanchoosefrom.Acommonadvantageofthesealgorithms
2.3 Mergingdetectedvoxelsintosources
istheabilitytolookforemissiononmultiplescales,whichises-
sentialtodetectsourcesin3D(seeFig1).Anexceptionisthesim- Theaforementionedbinarymaskisthebasisforidentifyingindi-
plethresholdmethod(seebelow),unlessusedincombinationwith vidualsourcesorobjects.InSoFiA,thiscomputationallyexpen-
someofthefilteringmethodsdescribedabove(e.g.,2D-1Dwavelet siveoperationisperformedusingtheC++implementationofthe
denoising).ThefollowingalgorithmsareimplementedinSoFiA. Lutz(1980)one-passalgorithmbyJurek(2012),combinedwitha
sparse representation of 3D objects. We refer to Jurek (2012) for
• Simplethreshold.Thisisthesimplestpossiblealgorithm(and
detailsonthisimplementation.Hereitissufficienttosaythatthis
theonlyonenotoperatingonmultiplescales):onlyvoxelswhose
algorithmproducesthesameresultasafriends-of-friendsmethod
absolute value is above a specified threshold are detected. Users
withlinkingelementequaltoanellipticcylinder.Userscanspecify
canspecifythethresholdinfluxunitsorrelativetothenoiselevel.
thecylindersize.ThisstepofSoFiAalsoreturnsbasicsourcepa-
• S+C.Thisisthesmooth+clipalgorithmdevelopedbySerra
rameterssuchastotalflux,peakflux(bothnormalisedbythenoise
et al. (2012) on the basis of techniques traditionally used within
level)andsize.
the HI community. It consists of searching for emission at mul-
ThebottompanelsofFig.4showtheobjectscreatedfromthe
tipleangularandvelocityresolutionsbysmoothingthedatacube
binarymaskusingamergingcylinderwitharadiusof3pixelsand
with 3D kernels specified by the user. At each resolution, voxels
a height of 7 channels (we show only objects with positive total
are detected if their absolute value is above a threshold given by
flux).Thesepanelsshowfourrealdetectionsaswellasanumber
theuser(innoiseunits).Thefinalmaskistheunionofthemasks
ofpositivenoise-peakobjects.Itisworthhighlightingthesuccess-
constructedatthevariousresolutions.
fuldetectionofafaint,extendedHItaileastofthebrightestgalaxy
• CNHI.ThisalgorithmwasdevelopedbyJurek(2012).Indi-
(second panel from the left). This detection is made possible by
vidual 1D spectra (or bundles of adjacent spectra) are extracted
thefactthatSoFiAlooksforemissiononmultiplescales.Further-
from the data cube. For each of them, the Kuiper test is used to
more, SoFiA correctly identifies as a single source the resolved,
identifyregionsofthespectrumwhicharenotconsistentwithcon-
edge-ongalaxylocatedinthesouthernpartofthecube(visiblein
tainingonlynoise.Inpractice,usersneedtoprovideaprobability
allpanelsbutthefirst)despitethelowlevelemissionatchannels
thresholdabovewhichaspectralregionisconsidereddetectedand
closetothesystemicvelocity.
isaddedtothefinalbinarymask.
Thenumerouspossiblecombinationsofthesesource-findingmeth-
2.4 Reliabilityandrejectionoffalsedetections
odstogetherwiththefilteringalgorithmsdescribedinSec.2.1al-
lowuserstodesignanumberofdifferentstrategiestodetectsignal Alldetectionalgorithmslistedaboverequireuserstospecifyade-
intheirdatacube.Forexample,theCNHIfindercouldberunfol- tectionthreshold.Thecloserthisthresholdistothenoise,themore
lowing convolution with a 3D kernel appropriate for the type of noise peaks will be included in the resulting binary mask. Some
sources being searched. Alternatively, a simple threshold method of these noise peaks may be identified as separate objects if they
couldbeusedafterthenoisehasbeenremovedfromthecubeby aresufficientlyfarfromarealobject(seebottompanelsofFig.4).
the2D-1Dwaveletfilter. SoFiA offers two ways of removing these false detections from
Popping et al. (2012) discuss strengths and weaknesses of thefinaloutput.
thesealgorithmsandcomparetheirperformance.Animportantrec- Thefirstmethodisasimplesizefilterandisbasedonthefact
ommendationofthatworkisthatallsourcefindersshouldincorpo- thatallrealdetectionsareatleastaslargeasthedatacube’sresolu-
ratesomeformof3Dsmoothinginordertoincreasecompleteness. tion.Inpractice,userscanspecifytheminimumacceptablesource
Inthisrespect,thesimplethresholdalgorithmisoflimiteduseun- size along each axis of the cube independently. The downside of
less coupled with a filtering methods such as the 2D-1D wavelet thismethodisthatitmaypotentiallyremoverelativelybrightbut
de-noising.Poppingetal.(2012)findthisparticularcombination unresolvedsourcesfromthefinalobjectmask.
(cid:13)c 2013RAS,MNRAS000,1–9
SoFiA3Dsourcefinder 5
1110.3 km/s 1234.0 km/s 1357.7 km/s 1481.3 km/s 1605.0 km/s
+62.3°
+62.2°
Dec (J2000)+62.1°
+62.0°
+61.9°
1110.3 km/s 1234.0 km/s 1357.7 km/s 1481.3 km/s 1605.0 km/s
+62.3°
+62.2°
Dec (J2000)+62.1°
+62.0°
+61.9°
180.8° 180.6° 180.4° 180.2° 180.8° 180.6° 180.4° 180.2° 180.8° 180.6° 180.4° 180.2° 180.8° 180.6° 180.4° 180.2° 180.8° 180.6° 180.4° 180.2°
RA (J2000) RA (J2000) RA (J2000) RA (J2000) RA (J2000)
Figure4.IllustrationofthedetectionofsignalandidentificationofindividualsourcesinSoFiA.Toppanels.Channelmapsextractedfromthedatacube
showninFig.1.Theline-of-sightvelocityofeachchannelisindicatedinthetop-leftcorner(notethatthesearenotadjacentchannelsintheoriginalcube).
Thebeamisshowninthebottom-leftcorner.Blackcontoursshowregionsincludedinthebinarymask(Sec.2.2).Bottompanels.Samechannelmapsasin
thetoppanelsbutnowshowingtheindividualobjectsformedonthebasisofthebinarymask(Sec.2.3).Weshowonlyobjectswithpositivetotalflux.Each
objectisindicatedwithadifferentrandomcolour.Blackcontoursindicatethefourobjectswhosereliabilityishigherthan99percent(Sec.2.4).
The second method is illustrated by Serra, Jurek & Flo¨er However, experience shows that masks can miss the faint, outer
(2012)andestimatesthereliabilityofindividualobjectsbycom- edge of objects, in particular if obtained with a high detection
paringthedistributionofpositiveandnegativesources(i.e.,sources threshold.Thiswouldintroducesystematiceffectsinthemeasured
with positive and negative total flux, respectively) in parameter parameters(e.g.,thetotalfluxwouldbeunderestimated;seeWest-
space.Thesimpleideaisthatthedistributionofpositiveandneg- meier,Popping&Serra2012).Topreventthis,SoFiAofferstwo
ativenoisepeaksshouldbeidenticalwhilepositive,realdetections maskoptimizationmethodswhichmodifytheobjectmaskcubeby
should not have a negative counterpart in parameter space. It is growingthemaskswhichdefineindividualobjects.Inbothmeth-
basedontheassumptionsthatthenoiseissymmetricandthatreal ods,themaskisgrownindependentlyforeachobject.
sourceshavepositivetotalflux(i.e.,absorptionlinesourceshave
beenmasked). Thefirstmethodismostlyappropriateforsourcesthatareun-
WithinSoFiA,thereliabilitycanbecalculatedfollowingthe resolvedontheskyor,ifresolved,face-onandsymmetric.Itstarts
runofanysource-findingalgorithmchosenbytheuseraslongas byfittinganellipsetothemoment-0imageoftheobject.Theel-
both positive and negative noise peaks are included in the binary lipseisthenusedasamaskforallvelocitychannelsoccupiedby
mask,andafterthedetectedvoxelsaremergedintosources(Sec. theobject–i.e.,theinitialmask,whichgenerallyhasanarbitrary
2.3).Thereliabilitycalculationalsorequiresthatasufficientnum- 3Dshape,isconvertedintoanellipticcylinder.Finally,thesizeof
berofnegativenoisepeaksisincludedinthemasksuchthattheir theellipseisincreaseduntilamaximumintotalfluxisreached(a
distributioninparameterspacecanbestudiedmeaningfully.Users similarmethodisdescribedbyBardenetal.2012inthecontextof
canselecttoproducediagnosticplotsonthereliabilitycalculation 2Dimaging).
similartothoseshowninSerra,Jurek&Flo¨er(2012).Theblack
The above method should in principle be applied only to
contoursinthebottompanelsofFig.4highlightobjectswhosere-
sourceswhichfillmostofthecylindricalmaskinallchannels(see
liabilityishigherthan99percent.
above),whileforobjectswithamorecomplex3Dstructureitcan
Insummary,userscandecidetorunSoFiAwithahighdetec-
resultinadecreaseoftheintegratedsignal-to-noiseratio.Forthis
tionthreshold,resultinginareliablebutpossiblyincompletecata-
reasonweprovideasecondmaskgrowthmethod.Thisconsistsin
logueofdetections;buttheycanalsodecidetodigdeeperintothe
performingabinarydilationoftheinitialmaskalongthetwospa-
noiseusingalowerthreshold,andsuccessivelyremovefalsedetec-
tialaxesofthedatacubeusinga2Ddilationstructuringelement
tions. In the latter case, a reliability value can be returned for all
whoseshapeapproximatesacircle.Thesizeofthestructuringele-
positivedetections.
mentisincreasediterativelyuntilthetotalfluxconverges(i.e.,until
therelativefluxgrowthbetweensuccessiveiterationsislowerthan
a threshold specified by the user). This method preserves the 3D
2.5 Maskoptimization
shapeoftheinitialmask.Inadditiontogrowthalongthetwospa-
SoFiAmeasurestheparametersofallsources(e.g.,totalflux,size, tialaxes,thisalgorithmcanalsogrowallmasksbyafixednumber
line width) considering only voxels included in the mask cube. ofchannels(selectedbytheuser)alongthefrequencyaxis.
(cid:13)c 2013RAS,MNRAS000,1–9
6 PaoloSerraetal.
+62.2° 400 0.20
1
Dec (J2000)+62.1° velocity (km/s) 0 1200 1300 F(Jy)000...011505
0
1
1
0.00
180.7° 180.6° 180.5° 180.4° 180.7° 180.6° 180.5° 180.4° –0.1 –0.05 0 0.05 0.1 1000 1100 1200 1300 1400
RA (J2000) RA (J2000) offset (deg) velocity(km/s)
Figure5.DataproductsforthebrightestgalaxyinthecubeshowninFig.1.Fromlefttoright:moment-0image;moment-1velocityfield;position-velocity
diagramalongthemorphologicalmajoraxis(PA=32◦);andintegratedspectrum(filledcircles)withthebest-fittingbusyfunctionoverlaid(solidline).Inthe
latterpanelthedottedanddashedlinesindicatethelinewidthsW50andW20estimatedat50and20percentofthepeakflux,respectively,onthebasisofthe
busyfunctionfit.
2.6 Sourceparameterization 2.8 PerformanceofSoFiA
As mentioned in Sec. 2.3, basic source parameters are measured InthecurrentimplementationofSoFiAtheentireinputdatacube
whendetectedvoxelsaremergedintoobjects.Thesecanbeused (or the selected sub-cube; see Fig. 2) is loaded into memory and
toestimatethereliabilityofeachsourceandrejectfalsedetections processed on a single core. Additional cubes will also need to
inparameterspace.AftermaskoptimizationSoFiAre-computes be stored in memory at various stages of processing, such as the
thoseparametersandmeasuresadditionalones.Theseinclude:po- weightscube,thebinaryorobjectmaskcube,andasmoothedver-
sition (both geometric and centre of mass); total flux; minimum sion of the data cube if required by the source-finding algorithm
and maximum voxel value; size and bounding region along each beingused(e.g.,S+C),plusapotentiallylargearrayofsourcepa-
axis; line width measured using different methods (including the rameters.Itisthereforeinterestingtodiscusshowthememoryre-
one proposed by Courtois et al. 2009); results of an ellipse fit to quirementandexecutiontimeofSoFiAvarywithcubesize.For
themoment-0image;resultsofabusyfunctionfittotheintegrated thispurposewemakeuseoftwocubes.Thesmallercubeistheone
spectrum(foradescriptionofthebusyfunctionseeWestmeieretal. usedforillustrationpurposeinthispaper(Figs.1and4).Ithas360
2014).Theseparametersareprovidedbothina“raw”format(i.e., pixelsalongbothspatialaxesand150channelsalongthefrequency
coordinatesinpixelunits,fluxesindataunits,line-widthinchan- axis,resultinginafilesizeof78MB.Thesecondcubeistheone
nels) as well as converted into more useful units (e.g., WCS co- usedforthesource-findingtestsofSerra,Jurek&Flo¨er(2012)and
ordinatesandstandardfluxandvelocityunits).Someofthesepa- Westmeier, Popping & Serra (2012). It too has 360 pixels along
rameterizationstepsareoptionalandimplementationofadditional bothspatialaxesbutconsistsof1464channelsalongthefrequency
parametersisstraightforwardwithinthecode. axis.Therefore,itssizeis∼10timesthatofthefirstcube.
We process the two cubes with identical settings employing
a representative combination of the algorithms described in this
paper: noise normalisation along the frequency axis; S+C source
finding with 12 smoothing kernels; merging of detected voxels
2.7 Outputproducts
into sources; calculation of reliability and removal of unreliable
Users can decide what output SoFiA should produce. Available sources; optimization of the mask of individual objects using the
outputproductsinclude: dilation method; source parameterization including busy function
fit;creationofoutputproductsforthecubesasawholeandforthe
• Catalog of objects and their parameters, both in ASCII and individualdetections;creationofASCIIandXMLcatalogues.The
VO-compliantXMLformat. tworunsarecarriedoutonamachinerunningLinuxMint17with
• Finalobjectmask. amemoryof16GBanda2.9GHzIntelCoreprocessor.
• Moment 0 and 1 images of the sky area covered by the full Figure6showsthememoryusageofSoFiAasafunctionof
datacubedeterminedfromthedatawithinthemask. time for the two cubes. Both axes of the plot are normalised by
• Cut-out data cubes containing individual objects as well as thecubesize.Thetimebehaviourofthetwocurvesappearsvery
their corresponding mask, moment 0, 1 and 2 images, integrated similar,indicatingthattheexecutiontimescalesapproximatelylin-
spectrum and position-velocity diagram along the morphological earlywithcubesizewithintherangeexploredhere.Thememory
majoraxis.AnexampleoftheseproductsisshowninFig.5. offsetbetweenthetwocurvesisduetotheloadingintomemoryof
anumberoflibrariesusedbySoFiA.Thesecomewithamemory
Infuturereleasesitwillbepossibletoproducetheseproductsfor overheadoftheorderofafewtensofmegabytes,whichismore
just a subset of the detections by selecting a region of interest in noticeableinthecaseofasmallerdatacube.Fordatacubesmuch
sourceparameterspace. larger than this overhead the memory usage is between 2 and 3
This output is designed to not only give useful information timesthesizeofthecube,withoccasionalpeaksbetween3and4
aboutthedetectedsourcesbutalsotoenablefurther,higher-level timesthecubesize.
analysisbytheuser.Forexample,thecut-outcubesofindividual Figure6allowsustoinvestigatethememoryandprocessing
objectsandthecorrespondingmaskscouldbeusedtomeasuread- timetakenbythevariousalgorithms.Inthiscase,mostofthetime
ditional source parameters not included in SoFiA or to produce istakenbytheS+Cfinder.Thebeginningandendofitsexecution
Gauss-Hermitevelocityfieldstoenablekinematicalstudies. aremarkedbyopenandfilledblackcirclesforthesmallandlarge
(cid:13)c 2013RAS,MNRAS000,1–9
SoFiA3Dsourcefinder 7
5
sizecube=79MB
sizecube=759MB
4
e
b
u
ec3
z
si
/
y
r
o 2
m
e
m
1
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6
time/size (s/MB)
cube
Figure6.MemoryusageasafunctionoftimefortworunsofSoFiAontwocubeswhosesizesdifferbyafactor∼10(seelegend).Asexplainedinthetext,
bothrunsincludetheuseoftheS+Csourcefinder,andopenandfilledblackcirclesindicatethebeginningandtheendoftheS+Cexecutionforthetwocubes,
respectively.SeeSec.2.8foramoredetaileddiscussionofthetimetakenbyotheralgorithmsduringthetwoSoFiAruns.
datacube,respectively.ThepeaksinmemoryusageofS+Ccorre- thatitallowsuserstosearchforemissioninanynumberofsmall
spondtothesmoothingoperations,whiletheplateausinbetween sub-cubescentredatasetof3Dcoordinateswithinanarbitrarily
peakscorrespondtothenoiselevelcalculation.Eachadditionalfil- large data cube. For example, in an era of large HI and optical
ter would contribute another ∼ 0.05 s/MB to the execution time redshiftsurveys,thismodecouldbeusedtolookforemissionin
inthiscase.Thenoisecalculationappearstobeparticularlytime alarge HI cubeatthelocationofgalaxiesincludedinanoptical
consuming.Inthiscase,itiscarriedoutusingtheaforementioned spectroscopiccatalogue.
Gaussianfittothenegativesideoffluxhistogram(Sec.2.1).This ThismodeisfullyintegratedinSoFiAandinterestedusers
calculationusesthefullcube,andanobviouswaytoincreaseits needtosimplyprovidetheinputdatacubeandacatalogueof3D
speedwouldbetocalculatethenoiselevelonasub-cube.Thisop- coordinates.SoFiAwillprocessthevariouspositionssequentially,
tionmaybecomeavailableinthefuture. eachtimeloadingintomemoryonlythesub-cubeofinterest.The
ThetimebeforethebeginningoftheS+CfinderinFig.6is 3Dsizeofthesub-cubescanbesetbytheuserandisthesamefor
takenbythenoisenormalisationalongthefrequencyaxisandby allpositions.Userscanalsorequestthecreationofasingleoutput
an initial measurement of the noise level in the normalised cube. catalogueofsources,whichisgeneratedbymergingthecatalogues
The time after S+C is taken by all other algorithms listed above, obtainedateachposition.
andthesearetypicallymuchfaster.Thememorypeakrightatthe
endofS+Ccorrespondstothemergingofvoxelsintosources.The
heightofthispeakdependsonthenumberofsourcesdetected.This
2.10 Comparisontoothersourcefinders
isfollowedbythecalculationofthereliabilityandtherejectionof
unreliablesources,whicharebothrelativelyinexpensiveinterms Anumberofestablishedsoftwarepackagesforthereductionand
of memory but can be time consuming. The final memory peaks analysis of interferometric data allow some source finding to be
correspondtothecreationofmomentimages. carriedoutondatacubes(e.g.,GIPSY,Miriad).However,this
approachrequiresuserstodevelopcustomcodeswhichmakeuse
of (and are limited by) the tasks available within those general-
purposepackages.Incontrast,themorespecialisedSoFiAoffers
2.9 Source-findingbasedonacatalogueof3Dcoordinates
awiderangeofready-to-usesource-findingalgorithms,whichare
The above discussion makes it clear that SoFiA is currently not alreadyintegratedwithoneanotherandcanbecombinedinaflex-
able to process arbitrarily large data cubes but is limited by the iblewaytoproduceavarietyofoutputproducts.
memoryofthesystemonwhichitisrun.Thisproblemispartially Theother3Dapplicationforspectrallinedatawhichshares
alleviatedbythefactthatSoFiAisabletolimittheprocessingto some of these characteristics is Duchamp (Whiting 2012). This
asub-cubewhoseboundariesarespecifiedbytheuser.Therefore, applicationdetectssourcesusingasimplethresholdmethod(sim-
users could choose to run SoFiA multiple times on sufficiently ilartotheonedescribedinSec.2.2)andthengrowsthemusinga
small portions of a large input cube, obtaining individual output secondarythreshold.Thisalgorithmdiffersfromthoseavailablein
productsforeachofthem.Theycouldthencombinetheseproducts, SoFiAand,inthisrespect,thetwopackagescouldbeseenascom-
creatingforexampleasinglemaskorcatalogue.Inthefuturewe plementary(Poppingetal.2012showsthatDuchamphasthebest
may be able to offer such breaking up of a large input cube into performance for unresolved sources but does not reach the com-
sub-cubes–andthecreationoffinaldataproductsforthefullcube pleteness of S+C for resolved sources). With respect to memory
–asaprocessingmodefullyintegratedwiththeothermodulesof requirements, Duchamp is similar to SoFiA in that it loads and
SoFiA. processesinonecorethefullinputdatacube.Therefore,ittoois
Inthiscontext,ausefulfeaturealreadyavailableinSoFiAis limitedbythememoryofthesystemonwhichitisrun.
(cid:13)c 2013RAS,MNRAS000,1–9
8 PaoloSerraetal.
AsignificantadvantageofSoFiAcomparedtoDuchampis sources.Thisoutputisdesignedtobothprovideausefuldescrip-
that it offers a larger number of algorithms for both source find- tionofthesourcesaswellasfacilitatesubsequentanalysis.
ingandparameterization.ThisincludestheS+CandCNHIfinders, WehighlightthemodularityofSoFiA,whichallowsusersto
the2D-1Dwaveletde-noising(denoisingisavailableinDuchamp optimize the source-finding and parameterization strategy for the
butitusesisotropicwavelets,whicharenotidealforspectralline data and sources of interest. This modularity also enables future
sources whose size along the spectral axis is decoupled from the expansionsofSoFiAtoincludenewsource-findingandparame-
sizealongthetwospatialaxes),thecalculationofthereliabilityof terisationalgorithms.
individualdetections,themaskoptimizationbybinarydilation,the SoFiA is publicly available at the website indicated in Sec.
possibilityofsearchingforsignalonthebasisofaninputcatalogue 1togetherwithtechnicalinformationonhowtousethesoftware.
of3Dcoordinatesandthebusyfunctionfit.Thecreationofcubelets Softwareupdates,improvementsandbugfixesarepostedregularly
andPVdiagramsforindividualdetectionsisalsonotincludedin at this webpage. SoFiA is registered at the Astrophysics Source
DuchampbutisavailableinSelavy,asourcefinderbuiltupon CodeLibrarywithIDascl:1412.001.
Duchamp for distributed processing of large cubes (Whiting &
Humphreys2012).Whilefuturedevelopmentmayreducethedif-
ference between Duchamp/Selavy and our package, all above
ACKNOWLEDGMENTS
methodsareatthemomentuniquetoSoFiA.
Finally,itisworthmentioningthatSoFiAdoesnotofferat TheauthorsacknowledgefinancialsupportfromaResearchCol-
themomentafullanalysisofthesources’morphology.Forexam- laborationAwardoftheUniversityofWesternAustralia.TvdHand
ple,agroupofnearbydetectedvoxelsismergedintoasinglesource NGweresupportedbytheEuropeanResearchCouncilunderunder
regardlessofthesizeofthesourceandonlybasedonthemerging theEuropeanUnion’sSeventhFrameworkProgramme(FP/2007-
elementchosenbytheuser(Sec.2.3).Thismeansthatnoinforma- 2013)/ERCGrantAgreementnr.291531.LFacknowledgessup-
tionisgivenaboutwhetherthesource,whichcouldbeverylarge, portbytheDeutscheForschungsgemeinschaft(DFG)undergrant
iscomposedofdistinctandeasilyrecognisablecomponents.Dif- numbers KE757/7-1, KE757/7-2, KE757/7-3 and KE757/9-1. LF
ferentandmorespecialisedsourcefindersareabletoprovidesuch isamemberoftheInternationalMaxPlanckResearchSchool(IM-
characterisation(e.g.,ClumpfindbyWilliams,deGeus&Blitz PRS)forAstronomyandAstrophysicsattheUniversitiesofBonn
1994;BLOBCATbyHalesetal.2012).Wenotehoweverthatthe andCologne.
objectmaskcubereturnedbySoFiAcouldbeusedasastarting
pointforfurthermorphologicalanalysisofthedetections.
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