MULTI-FREQUENCY SYNTHESIS TECHNIQUE IN RADIO INTERFEROMETRIC IMAGING USING GENERALIZED MAXIMUM ENTROPY METHOD

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MULTI-FREQUENCY SYNTHESIS TECHNIQUE IN RADIO
INTERFEROMETRIC IMAGING USING GENERALIZED MAXIMUM
ENTROPY METHOD

• Anisa T. Bajkova
• Central (Pulkovo) Astronomical Observatory of RAS

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MFS in VLBI assumes mapping at several observing
radio frequencies simultaneously to improve
UV-coverage, so MFS is a tool of rapid aperture
synthesis. MFS is possible due to measurement of
UV-coordinates of visibility function in
wavelengths. The main problem of MFS is spectral
dependence of a source brightness distribution
and in order to avoid possible artifacts in the
image it is necessary to fulfill spectral
correction during the deconvolution stage of the
image formation (CLEAN or MEM) .
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The most important works on MFS

1. Conway, J.E., Cornwell T.J., Wilkinson P.N.
   MNRAS, 1990, 246, 490.
2. Conway, J.E. Proc. IAU Coll. 131, ASP Conf.
   Ser., 1991, 19, 171.
3. Cornwell, T.J. VLB Array Memo 324, 1984, NRAO,
   Socorro, NM.
4. Sault, R.J., Wieringa, M.H. A A, Suppl. Ser.,
   1994, 108, 585.
5. Sault, R.J., Oosterloo, T.A. astro-ph/0701171v1,
   2007.
6. Likhachev, S.F., Ladygin, V.A., Guirin, I.A.
   Radioph. Quantum Electr., 2006, 49, 499.

are based on CLEAN deconvolution algorithm for
spectral correction of images (double-deconvolutio
n algorithm 1,2,4,5, vector-relaxation
algorithm 6).
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The aim of this work

• Development and investigation of a
  new MFS deconvolution algorithm based on maximum
  entropy method for effective solving spectral
  variation problem in broad-band frequency region
  and estimation of a spectral index distribution
  over a source.

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CLEAN or MEM ?
Bob Sault

• The answer is image dependent
• High quality data, extended emission, large
  images
• ? Maximum entropy
• Poor quality data, confused fields, point
  sources ? CLEAN

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Importance of MFS for Russian Radio Astronomy

• Three-element Russian
• Quasar VLBI network (Svetloye,
  Zelenchukskaya, Badary)
• Future Space-Ground
• high-orbit Radioastron
• mission
• In both cases we have sparse UV- coverages,
  insufficient for imaging radio sources with
  complicated structure

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Improving UV-coverage
(a)
(b)
Four element radio Interferometer Svetloe,
Zelenchukskaya, Badary, Matera (a) single
frequency synthesis (b) multi-frequency
synthesis

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Space-Ground Radio Interferometer Radioastron
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Spectral variation
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Bob Sault
Maximum entropy image deconvolution
principle Of all the possible images
consistent with the observed data, the one that
has the maximum entropy is most likely to be the
correct one.
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Maximum Entropy Method
Discrete form of practical MEM
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Visibility function constraints
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Reconstruction using Generalized Maximum Entropy
Method (GMEM)
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The Lagrange method
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Solution
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Unconditional optimization problem
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Simulation results
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SFS
UV-planes
?
?
90
60
?
?
Fig.1
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a
b
c

Fig.2
Model distributions of the source (a), first
-order spectral map (b) and spectral index (c)
(0 lta(x,y)lt0.8), size of maps 128x128 Contour
levels 0.0625,0.125,0.25,0.5,1,2,4,8,16,32,64,99

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? ?
?
Fig.3
Reconstructed images using (a) SFS (b) ?FS
(30),a(x,y)0 (c) MFS a(x,y)?0 Contour levels
0.0625,0.125,0.25,0.5,1,2,4,8,16,32,64,99
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Io(x,y) I1(x,y)
a(x,y)
2
?
b c

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d
e f
Fig.4
(Frequency band30)
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2
?
b c

3
d
e f
4
Fig.5(60)
g
h
i
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2
? b
c
3
d
e f
4
Fig.6 (90)
g
h i
25
?
b c

Fig.7
MFS (90), 27 frequences
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SFS without spectral correction
2 3
?
b
c
d
4 5
I1(x,y) a(x,y)
e
f
h
i
???.8
MFS (90, 9 frequencies) significant noise in
data (visibility function) Contour levels
0.25,0.5,1,2,4,8,16,32,64,99
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Modelling 3C120
Model of 3C120 at 8.2 GHz
Spectral index distribution
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Reconstructed images -2.1 lta(x,y)lt0.8,
frequency bandwidth30, nonlinear spectral
correction with N4
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Reconstructed images -2.1 lta(x,y)lt0.8,
frequency bandwidth60, nonlinear spectral
correction with N4
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Modelling Radioastron mission
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SFS
MFS (bandwidth30) MFS
(bandwidth60)


UV-coverage for Radioastron mission (U,V in 108
wavelengths)
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Image synthesis by Radioastron
Model
SFS

MFS with spectral correction MFS without
spectral correction
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Image synthesis by Radioastron
Source model
SFS
MFS(30)(a(x,y)0)
MFS(30)( a(x,y)?0)
MFS(30)( a(x,y)?0)
MFS(60)( a(x,y)?0) (without
spectral correction) (linear
spectral correction N2) (nonlinear spectral
correction N4)

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CONCLUSION

• We proposed and investigated simple and
  effective MFS-deconvolution technique based on
  the Generalized Maximum Entropy Method which
  allows to provide accurate spectral correction of
  images in wide frequency band and reconstruct
  both source brightness and spectral index
  distributions.
• The results obtained will be published in
• Astronomy Reports (2008), v.85, N 12.

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THANK YOU FOR ATTENTION!