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SKAmachinelearningperspec1ves
SlavaVoloshynovskiy
Stochas1cInforma1onProcessingGroup
UniversityofGeneva
Switzerland
withcontribu,onof:
D.Kostadinov,S.Ferdowsi,M.Diephuis,O.TaranandT.Holotyak
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Outline
MachinelearningchallengesinSKA
Proposedapproach
Extensions
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Machinelearningreali1esandSKA
Newperspec,vesofmachinelearningbasedimageprocessingdueto:
§  largeamountofcollectedobserva1ons(trainingdata)
§  newpowerfulcomputa1onalfacili1es
§  modernphasedantennaarrays
§  op1misa1onalgorithms
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MainSKAchallenges
§  Challenge1:Imaging-reconstruc,on
§  Hugeamountofcomputa1onfor
pair-wisecorrela1ons,calibra1on,
reconstruc1on
§  Challenge2:Datatransferandstorage
§  Datatransferfromcorrelatorsto
reconstruc1onservers,datacenters,
SDPandendusers
§  Challenge3:Analy,cs
§  Automa1cprocessingofproduced
data(recogni1on,mining,search,
tracking,…)
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Imaging–genericapproach
Restora1on
p(x) Priorson Priorson
z
H
x (λ )
p ( x ( λ ))
H
p(y | x)
y = Hx + z
MAP
x̂
x̂ = arg max p(y x)p(x)
x
Mainissue:
p(x)
Howtomodeltoobtain
accurate,tractableandlow-complexitysolu1on?
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Imaging–“machinelearning”approach
Given:alotoftrainingdata
Learn:sta1s1calmodelp(x)
Physicalmodel x ( θ1, θ2,!θL )
Physicalphenomenon x
{ x ( λ1 )}
{ x ( λ2 )}
Variousimagingconfigura1ons
Radiowaves Microwaves
{ x ( λ3 )}
Infrared
{ x ( λ4 )}
Visible
{ x ( λ5 )}
Ultraviolet
{ x ( λ6 )}
X-Ray
Trainingdata
+Simula1ontools
Faraday,ASKAP,CASA..
ALMA,EVLA,LOFAR,VLBI,…,SKA
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“Hand-cra_ed”vsMachinelearning
Imaging:mainapproaches
“Hand-craUed”approaches
Machinelearningbasedapproaches
MAP
MAP
x̂ = arg max p(y x)p(x)
x
Smoothnessofsolu1on,localcorrela1ons…..
x
x(a)
y = Hx + z
y = Hx + z
x̂ = arg min y − Hx
x̂ = arg max p(y x)p(x a)p(a)
2
2
+ λΩ ( x )
Ω ( x ) = −ln p ( x )
⇒o_enunknown
p(x) ⇒verydifficulttodescribeanaly1cally
⇒definedsolelybasedonhumanexper1se
“Doubly”stochas1capproach
x̂ = arg min y − Hx
x(a)
2
2
+ λΩx,a ( x, a ) + τΩa ( a )
Synthesisapproach x = Φa + e
2
⇒ λΩx,a ( x, a ) = x - Φa 2
⇒ powerfulbutNP-hard
Transformlearning Wx = a + n
2
⇒ λΩx,a ( x, a ) = Wx - a 2
⇒ close-formsolu1on
⇒ scalable
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ImportanceforSKA:scalabilitytoBigData
Op,miza,onforSKA:
ScalabilitytoBigData(bothdimension/sizeandamount)
Low-complexitysolu,on(directproblemvsinverseone)
Lesstrainingdataneeded
Paralleliza,on
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ImportanceforSKA:learningfor“adap1ve”imaging
Op,miza,onforSKA:
Imagingapertureadapta,ontotargeteddata
Current:imagingarraygeometryandimagesarenotmatched(evenCS)
Consequences:
alotofmeasurementsarenotinforma,ve
hugeamountofcomputa,onalloadoncorrelatorsandreconstruc,on
enormousamountofdatatotransferandstore
Ourproposal:
Op,mizeimagingarraygeometrytodata(learningonfly)
( Ĥ, x̂ ) = arg min
H,x(a)
y − Hx
2
2
+ λΩx,a ( x, a ) + τΩa ( a )
underconstraintsonanumberofantennaarrayelementsandtheirpossibleposi1ons
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ImportanceforSKA:learningfor“adap1ve”imaging
GeometrySpa1alspectrum(uv-plane)PSF(direc1onalantennapahern)
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Imaging–learningfor“adap1ve”imaging
Non-adap,vesystems
Reconstruc1on
ℑ
x
!
x
y = Hx + z
x̂
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Imaging–learningfor“adap1ve”imaging
⇒
Objec,ve:minimizetheloadoncorrelatorsadap,ve“light-weight”imaging
! -es1ma1onconfigura1on(trained)
H
i
yi
Es1ma1onof
dominant
components
ℑ
x
Reconstruc1on
x̂
!
x
yj
! -adap1veconfigura1on
H
j
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Imaging–learningfor“adap1ve”imaging
Allelements“Matched”elementsResidual
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Extensions
§  Sta,s,calimageprocessingandmachinelearningfor:
§  High-resolu1onimaging(reconstruc1on,single-imagesuper-resolu1on)
§  Imagecompression(machinelearningbasedcodebookes1ma1on)
§  Analy1csforBigData(fastsearchinbigdatacollec1ons,dataanalysis,mining
ofdependenciesbetweenmul1modaldata,etc)
§  Designandop,miza,onoflargescaleimagingsystems
§  Minimiza1onofnumberofantennas,1me,etc