SKA machine learning perspec1ves for imaging, processing and analysis

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University of Geneva Switzerland with contribu,on of: D.

1 1 SKA machine learning perspec1ves for imaging, processing and analysis Slava Voloshynovskiy Stochas1c Informa1on Processing Group University of Geneva Switzerland with contribu,on of: D. Kostadinov, S. Ferdowsi, M. Diephuis, O. Taran and T. Holotyak Swiss SKA Day, EPFL

2 Outline Machine learning challenges in SKA Challenge 1 imaging-reconstruc1on Challenge data compression for transfer and storage Challenge 3 analy1cs and processing of big data Conclusions

3 3 Remark Compila,on of exper,se from Computer Science department Sec1on of mathema1cs Observatory

4 Machine learning reali1es and SKA 4 New perspec,ves of machine learning based image processing due to: large amount of collected observa1ons (training data) new powerful computa1onal facili1es modern phased antenna arrays op1misa1on algorithms

5 Main SKA challenges 5 Challenge 1: Imaging-reconstruc,on Huge amount of computa1on for pair-wise correla1ons, calibra1on, reconstruc1on Challenge : Data transfer and storage Data transfer from correlators to reconstruc1on servers, data centers, SDP and end users Challenge 3: Analy,cs Automa1c processing of produced data (recogni1on, mining, search, tracking, )

6 Challenge 1: Imaging generic approach 6 Restora1on x( λ) p( x( λ) ) H p(x) Priors on H Priors on z y = Hx + z p(y x) ˆx MAP ˆx = arg max x p(y x)p(x) Main issue: How to model p(x) to obtain accurate, tractable and low-complexity solu1on?

$Challenge 1: Imaging hand-cra\ed approach 7 Tradi,onal approaches to defini,on of p(x) Sta,s,cal/determinis,c approaches Direct domain Smoothness of solu1on, local correla1ons.$

7 Challenge 1: Imaging hand-cra\ed approach 7 Tradi,onal approaches to defini,on of p(x) Sta,s,cal/determinis,c approaches Direct domain Smoothness of solu1on, local correla1ons.. Ω a ˆx = arg min a Ω x y Hx + λω x ( ) Transform domain (decorrela1on, energy compac1on, direc1vity, ) â = arg min a y HDa + λω a ( ) ( ) = ln p( x ) ˆx = Dâ fixed, signal independent (DCT, DWT.) Ω( a ) = ln p( a ) Sparsity-based approach â = arg min a ( ) y HΨa + λω a ˆx = Ψâ Overcomplete and can be learned i.i.d. GGD i.i.d. Student i.i.d. Mixture of Gaussians etc ( ) = a Ω a 0 ( ) = a 1 Nonconvex and NP-hard problem: relaxa1o1on/greedy approaches Complex op1miza1on tools: proximal algorithms prime-dual methods augmented Langrangian...leading to parallel and distributed solu1ons

8 Challenge 1: Imaging machine learning approach 8 Physical model x( θ 1,θ,!θ L ) Given: a lot of training data Learn: sta1s1cal model p(x) Physical phenomenon x { x( λ 1 )} { x( λ )} { x( λ 3 )} { x( λ 4 )} { x( λ 5 )} { x( λ 6 )} Various imaging configura1ons Radiowaves Microwaves Infrared Visible Ultraviolet X-Ray ALMA, EVLA, LOFAR, VLBI,, SKA + Simula1on tools Faraday, ASKAP,CASA.. Training data

9 Challenge 1: Imaging as learning problem 9 a Ω( a ) Given: training data ( y j, x j ), 1 j K Reconstruc1on Ωab ( a, b) algorithm = mapper Transcoding ϕ (.) y x j j D d Learn a mapper ϕ (.)

10 Challenge 1: Imaging learning as encoding-decoding 10 Given: training data ( y j, x j ), 1 j K Encoder Decoder D d y j x j Split in two parts

11 Challenge 1: Imaging learning as encoding-decoding 11 Intermediate representa1on a ( ) Ω a b Given: training data ( y j, x j ), 1 j K D e ( a, b ) Ωab Ω ab Transcoding y x j j D d Encoder-decoder training ( ˆD e, ˆD d ) = arg min â = arg min a â = ψ D e y, ˆb ( ) K ˆD e, ˆD d a j D e y j j=1 Projec,on problem a D e y + γ1 Ω a Encoder + λ1 Ω a a j ( a ) + γ Ω ab ( a, ˆb ) Training ( ) + λ Ω ab ( a j, b j ) + λ 3 x j D d b j! ˆb = arg min a ˆx = D dˆb Decoder Reconstruc,on problem y D d b + λωab ϒ( D e, D d ) ( â, b)

Challenge 1: Imaging learning op1mal imaging configura1ons 1 Objec,ve: joint op,miza,on of reconstruc,on and imaging (CS random sampling) x j Imaging H D e Intermediate representa1on a Ω( a ) ( a, b)

12 Challenge 1: Imaging learning op1mal imaging configura1ons 1 Objec,ve: joint op,miza,on of reconstruc,on and imaging (CS random sampling) x j Imaging H D e Intermediate representa1on a Ω( a ) ( a, b) Ωab Transcoding y j x j b D d Training Imaging system-encoder-decoder training Encoder ( Ĥ, ˆD e, ˆD d ) = arg min K H, ˆD e, ˆD d a j D e Hx j j=1 + λ1 Ω a a j ( ) + λ Ω ab ( a j, b j ) + λ 3 x j D d b j Decoder ϒ( D e, D d ) Φ( H) constraints on number and possible geometry of synthesized arrays

h i - es1ma1on configura1on (trained) y i I x!

13 Challenge 1: Imaging learning for adap1ve imaging 13 Objec,ve: minimize the load on correlators adap,ve light-weight imaging!h i - es1ma1on configura1on (trained) y i I x!x Es1ma1on of dominant components Reconstruc1on ˆx y j!h j - adap1ve configura1on

Challenge : Compression for transfer, storage and

Compression x H y = Hx + z Alterna,ve - compressive sensing

image independent y = Q( Hx + z) observa1ons are quan1zed

14 Challenge : Compression for transfer, storage and distribu1on 14 Tradi,onal approach to compression Restora1on Compression x H y = Hx + z Alterna,ve - compressive sensing quan,zed compressive sensing ˆx JPEG ˆx JPEGK c Generic and image independent y = Q( Hx + z) observa1ons are quan1zed (even to several bits) ˆx = arg min a y Q( Hx ) + λω x ( ) - inverse problem

15 Challenge : Compression machine learning approach 15 Op,on 1: Replace generic JPEG/JPEGK codecs by special algorithms trained on RI images We suppose that the image is already reconstructed and the problem is how to deliver it to the end users Op,on : Sparse code representa,on between the Encoder-Decoder Encoder-decoder pairs in reconstruc1on are trained with the entropy constrained sparse code Efficient coding based on structured codebooks vs random ones Intermediate representa1on a b ( ) Ω a D e ( a, b) Ωab Transcoding D d y j x j

16 Challenge : Compression informa1on-theore1c approach 16 Codebook training (like Shannon R(D) theory) from p(x) 1 Codebook C Rate-distor,on plot n 1 M nr Informa1on-theore1c approach (limits) p(x) is not known Codebook size is exponen1al in n Codebook is unstructured High compression complexity and memory

Codebook C L n 1 M 1 M M L L trained codebooks (structured) Polynomial

17 Challenge : Compression machine learning approach 17 Structured codebooks with successive refinement Rate-distor,on plot 1 Codebook C 1 Codebook C Codebook C L n 1 M 1 M M L L trained codebooks (structured) Polynomial complexity Approaching Shannon lower bound Outperforming JPEG/JPEGK for very low bit rates

Ωab D d y j x j Feature vector = compact and discrimina1ve image representa1on Supervised

18 Challenge 3: Analy1cs automa1c processing of Big Data 18 Main issue: dimensionality and amount of images for automa,c processing Intermediate representa1on a b ( ) Ω a D e ( a, b) Ωab D d y j x j Feature vector = compact and discrimina1ve image representa1on Supervised hashing Recogni1on Data mining Search Indexing Automa,c tools for Big Data analysis

19 Conclusions 19 SKA is a great tool for research. and not only in astronomy and astro-physics It is a test planorm for many ideas in machine learning based image processing thanks to big data and flexible imaging In turns, it will lead to new alterna1ve approaches to three SKA challenges covering: imaging and reconstruc1on algorithms compression algorithms automa1c processing of big data

CS 6140: Machine Learning Spring What We Learned Last Week 2/26/16

Logis@cs CS 6140: Machine Learning Spring 2016 Instructor: Lu Wang College of Computer and Informa@on Science Northeastern University Webpage: www.ccs.neu.edu/home/luwang Email: luwang@ccs.neu.edu Sign