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