SKAmachinelearningperspec1ves
SlavaVoloshynovskiyStochas1cInforma1onProcessingGroup
UniversityofGenevaSwitzerland
1
withcontribu,onof:D.Kostadinov,S.Ferdowsi,M.Diephuis,O.TaranandT.Holotyak
Outline
MachinelearningchallengesinSKA
Proposedapproach
Extensions
2
Machinelearningreali1esandSKA3
Newperspec,vesofmachinelearningbasedimageprocessingdueto:
§ largeamountofcollectedobserva1ons(trainingdata)
§ newpowerfulcomputa1onalfacili1es
§ modernphasedantennaarrays
§ op1misa1onalgorithms
MainSKAchallenges4
§ Challenge1:Imaging-reconstruc,on§ Hugeamountofcomputa1onfor
pair-wisecorrela1ons,calibra1on,reconstruc1on
§ Challenge2:Datatransferandstorage§ Datatransferfromcorrelatorsto
reconstruc1onservers,datacenters,SDPandendusers
§ Challenge3:Analy,cs§ Automa1cprocessingofproduced
data(recogni1on,mining,search,tracking,…)
Imaging–genericapproach5
Restora1on
p x λ( )( )
H x λ( )
p(x) H
Priorson z
Priorson
p(y | x)
x = argmax
xp(y x)p(x)MAP
Mainissue:Howtomodeltoobtainaccurate,tractableandlow-complexitysolu1on?
p(x)
y = Hx + z x
Imaging–“machinelearning”approach6
Physicalphenomenon
Physicalmodel x θ1,θ2,!θL( )
x
Radiowaves Microwaves Infrared Visible Ultraviolet X-Ray
x λ1( ){ }
x λ2( ){ }
x λ3( ){ }
x λ4( ){ }
x λ6( ){ }
x λ5( ){ }
Given:alotoftrainingdataLearn:sta1s1calmodel
Vario
usim
agingconfi
gura1o
ns
ALMA,EVLA,LOFAR,VLBI,…,SKA
p(x)
+Simula1ontoolsFaraday,ASKAP,CASA..
Trainingdata
“Hand-cra_ed”vsMachinelearning7
Imaging:mainapproaches
“Hand-craUed”approaches
x = argmax
xp(y x)p(x)MAP
Machinelearningbasedapproaches
x = argmax
x(a)p(y x)p(x a)p(a)MAP
y = Hx + z
“Doubly”stochas1capproach
x = argmin
x(a)y−Hx
2
2+ λΩx,a x,a( ) + τΩa a( )
x = Φa + e
λΩx,a x,a( ) = x - Φa
2
2Synthesisapproach
⇒
⇒ powerfulbutNP-hard
Wx = a + n
λΩx,a x,a( ) = Wx - a
2
2Transformlearning
⇒
⇒ close-formsolu1onscalable ⇒
y = Hx + z
Smoothnessofsolu1on,localcorrela1ons…..
x = argmin
x
y−Hx2
2+ λΩ x( )
Ω x( ) = − ln p x( )
o_enunknownverydifficulttodescribeanaly1callydefinedsolelybasedonhumanexper1se
p(x) ⇒ ⇒ ⇒
ImportanceforSKA:scalabilitytoBigData8
Op,miza,onforSKA:
ScalabilitytoBigData(bothdimension/sizeandamount)
Low-complexitysolu,on(directproblemvsinverseone)Lesstrainingdataneeded
Paralleliza,on
ImportanceforSKA:learningfor“adap1ve”imaging9
Op,miza,onforSKA:
Current:imagingarraygeometryandimagesarenotmatched(evenCS)
Imagingapertureadapta,ontotargeteddata
Consequences:alotofmeasurementsarenotinforma,vehugeamountofcomputa,onalloadoncorrelatorsandreconstruc,onenormousamountofdatatotransferandstore
Ourproposal:Op,mizeimagingarraygeometrytodata(learningonfly)
H, x( ) = argmin
H,x(a)y−Hx
2
2+ λΩx,a x,a( ) + τΩa a( )
underconstraintsonanumberofantennaarrayelementsandtheirpossibleposi1ons
ImportanceforSKA:learningfor“adap1ve”imaging
10
GeometrySpa1alspectrum(uv-plane)PSF(direc1onalantennapahern)
Imaging–learningfor“adap1ve”imaging11
Non-adap,vesystems
x !x
ℑ
x
Reconstruc1on
y = Hx + z
Imaging–learningfor“adap1ve”imaging12
Objec,ve:minimizetheloadoncorrelatorsadap,ve“light-weight”imaging ⇒
!Hi
x !x
yi
-es1ma1onconfigura1on(trained)
ℑ
yj
!Hj
Es1ma1onofdominant
components
-adap1veconfigura1on
x
Reconstruc1on
Imaging–learningfor“adap1ve”imaging13
Allelements“Matched”elementsResidual
Extensions14
§ Sta,s,calimageprocessingandmachinelearningfor:
§ High-resolu1onimaging(reconstruc1on,single-imagesuper-resolu1on)§ Imagecompression(machinelearningbasedcodebookes1ma1on)§ Analy1csforBigData(fastsearchinbigdatacollec1ons,dataanalysis,mining
ofdependenciesbetweenmul1modaldata,etc)
§ Designandop,miza,onoflargescaleimagingsystems§ Minimiza1onofnumberofantennas,1me,etc