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A Model Based Approach to LOFAR Calibration and Imaging Stefan J. Wijnholds
e-mail: wijnholds@astron.nl

AAVP Workshop Cambridge (UK), 8 10 December 2010

AAVP Workshop, Cambridge, 8 10 December 2010

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The model based approach
Traditional approach

Model based approach

relation between visibility and image planes (FT) image plane vs. visibility plane corrections potential bias through assumptions involved computationally efficient

relation between data samples and image parameters arbitrary corrections per sample per image value possible accurate results typical complexity: N
3

AAVP Workshop, Cambridge, 8 10 December 2010

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Highlight: LOFAR station calibration
S.J. Wijnholds & A.J. van der Veen, IEEE TrSP, Sep. 2009 S.J. Wijnholds, Ph.D. thesis, 2 March 2010

phase solutions (left) and A/T improvement (right) typical: 860 params solved in 0.4s on single 2.4-GHz core

AAVP Workshop, Cambridge, 8 10 December 2010

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Least squares imaging
S.J. Wijnholds, SKA2010, 22 25 March 2010 S.J. Wijnholds, Ph.D. thesis, 2 March 2010

Least squares image estimation (OMM, ML estimation):

can handle arbitrary image plane effects (DDEs) can handle arbitrary visibility plane effects can handle non-sparse fields is statistically efficient on actual data becomes computationally feasible in SKA era can be easily integrated with calibration

Applications: confusion limited imaging, Galactic polarimetry, Galactic HI, EoR
AAVP Workshop, Cambridge, 8 10 December 2010 -4-

Highlight: DFT vs. LS imaging
S.J. Wijnholds, URSI Benelux Forum, 8 June 2009 S.J. Wijnholds, Ph.D. thesis, 2 March 2010

8 Nov. 2008, 10:21:59 10:26:45 UTC, 10 s integration 27 156-kHz subbands between 45.3 and 67.3 MHz

AAVP Workshop, Cambridge, 8 10 December 2010

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Processing and memory requirements
S.J. Wijnholds, SKA2010, 22 25 March 2010

Memory: Nim x Nim x 8 byte (in place processing) Processing: ~N
3 im

flop (not flops)

Numerical example: scalar imaging with the SKA core

D

core

= 5 km, D
core

dish

= 15 m (AA stations are larger)

Nim = ((D

/ Dstation) / 0.7)2 = 2.27 x 105

memory: 411.4 GB processing: ~11.7 Pflop to compute in 4h: 809.7 Gflops
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AAVP Workshop, Cambridge, 8 10 December 2010

Range of applicability
S.J. Wijnholds, SKA2010, 22 25 March 2010

scalar size memory 128x128 256x256 512x512 1024x1024 2048x2048 4096x4096 2.15 GB 34.4 GB 550 GB 8.80 TB 141 TB 2.05 PB

processing ~4.40 Tflop ~281 Tflop ~18.0 Pflop ~1.15 Eflop ~73.8 Eflop ~4.72 Zflop

flops in 4h 306 Mflops 19.5 Gflops 1.25 Tflops 79.9 Tflops 5.13 Pflops 328 Pflops

N3 algorithms feasible for SKA core!
AAVP Workshop, Cambridge, 8 10 December 2010 -7-

SP example: KL-transform
S.J. Wijnholds & A.J. van der Veen, ICASSP 2011, submitted

LS-image vs. KL-image with 3 times higher resolution Computed on laptop using 1361 out of 8937 components

AAVP Workshop, Cambridge, 8 10 December 2010

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Calibration & imaging questions
Wijnholds, Grainge and Nijboer, discussion 30 Nov. 2010

How should we deal with TDDEs?

ionosphere varying beam shapes

How do we measure / track these TDDEs? How do we deal with strong sources? How should we deal with mutual coupling? How accurate should we know the beam shape? How accurate should we calibrate the system? Etc.
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AAVP Workshop, Cambridge, 8 10 December 2010

Conclusions
Model based approach

allows arbitrary corrections between data and params no simplifying assumptions needed typical complexity N
3

feasible in SKA era, at least for core area demonstrated on LOFAR station processing will be used for LOFAR EoR (Ph.D. Lambropoulos)

Feasibility O(N3) allows for many SP techniques! Many interesting calibration & imaging challenges!
AAVP Workshop, Cambridge, 8 10 December 2010 - 10 -