direct imaging and feature extraction of bh shadows with ... · with the eht kazuki kuramochi...
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Direct Imaging and Feature Extraction of BH Shadows
with the EHT
Kazuki Kuramochi (Tokyo Univ./NAOJ)
CollaboratorsKazunori Akiyama (NRAO/MIT Haystack), Shiro Ikeda (Institute of
Statistical Mathematics), Fumie Tazaki, Mareki Honma (NAOJ), Vincent L. Fish (MIT Haystack), Hung-Yi Pu (Perimeter Institute for
Theoretical Physics), Keiichi Asada (ASIAA)
Background: Gargantua (© interstellar 2014 )
01/27/2018 AGN-jet workshop in Tohoku U
Investigation of the event horizon scales
Obtain “beautiful” images of the BH shadow = Great advantage to investigate relating to BHs
• BH images depend on parameters relating to the black hole⇒ Estimate parameters with BH images
• BH images change due to time variabilities⇒ Find the origin of time variabilities with BH images
(Chael et al. 2016)
CLEAN
(Akiyama et al. 2017a)
CLEAN is problematic for the BH shadows
01/27/2018 AGN-jet workshop in Tohoku U
Previous work: Sparse modeling• Find the best solution on the assumption of sparsity• Regularize the image with L1 norm (e.g. LASSO)
Consistency with data
Sparsityof the image
Ground truth (convolved) SpM image(Honma et al. 2014)
※SpM image isconvolved withrestoring beam
01/27/2018 AGN-jet workshop in Tohoku U
Previous work: Sparse modeling• Find the best solution on the assumption of sparsity• Regularize the image with L1 norm (e.g. LASSO)
Ground truth CLEAN image L1 image(Failure case; Akiyama et al. 2017b)
Consistency with data Sparsity of the image
01/27/2018 AGN-jet workshop in Tohoku U
Previous work: Smoothing regularizerSolution• New regularizer: isotropic Total Variation (TV) term
(Rudin et al. 1992)• Adjust sparsity on the gradient domain (= smoothness)
Form:
Ground truth L1 image(M87; Akiyama et al. 2017b)
L1+TV image
01/27/2018 AGN-jet workshop in Tohoku U
Issues: Edge-preserving regularization
Issues1. Emission structures are overbroad and overflatter
⇒ The apparent shadow size is underestimated2. Edges of structures are over-enhanced“edge-preserving” regularization
Ground truth L1+TV image
SuitableNOT suitable…
01/27/2018 AGN-jet workshop in Tohoku U
Solution: Edge-smoothing regularizer
Solution• New regularizer: Total Squared Variation (TSV) term
“edge-smoothing” regularization
Form:
⋯𝒙𝒙𝒊𝒊
TV term
𝒙𝒙𝒊𝒊+𝟏𝟏 𝒙𝒙𝒊𝒊+𝟐𝟐
TSV term
Results are consistent between two terms
01/27/2018 AGN-jet workshop in Tohoku U
Simulations• Simulate observations with the EHT 2017’s array• Reconstruct images with L1+TV regularization and
L1+TSV one• Compare the performance of two regularizations
Sub-Keplerian KeplerianTheoretical model (Pu et al. 2016)𝒖𝒖𝒖𝒖 coverage
01/27/2018 AGN-jet workshop in Tohoku U
Results: Image appearance• L1+TSV images are more similar to ground truth than
L1+TV ones
Sub-KeplerianL1+TV image L1+TSV imageGround truth
01/27/2018 AGN-jet workshop in Tohoku U
Results: Image appearance• L1+TSV images are more similar to ground truth than
L1+TV ones
KeplerianL1+TV image L1+TSV imageGround truth
01/27/2018 AGN-jet workshop in Tohoku U
Results: Optimal resolution• L1+TSV images are more similar to ground truth than
L1+TV ones• (Perhaps) Restoring beam is no longer necessary for
imaging due to L1+TSV regularization
Sub-Keplerian
Ground truth
L1+TSV
high
←Im
age
qual
ity →
low
Restoring Beam/CLEAN Beam
L1+TV
01/27/2018 AGN-jet workshop in Tohoku U
Prospect for the EHT: Detection of the shadow
• BH images depend on parameters relating to the black hole (e.g. Broderick et al. 2011a, b)⇒ Detection of the BH shadow from the reconstructed image with the Circular Hough Transform (CHT)
ApplyBH
shadow?
Orig
inal
Resu
lt
01/27/2018 AGN-jet workshop in Tohoku U
Prospect for the EHT: Detection of the shadow
ResultWe can estimate the size of the BH shadow within ~10-20%
low
←Pr
obab
ility
→ h
igh
Radius (𝝁𝝁as)
Ground truth
SpM~20%
Sub-Keplerian
01/27/2018 AGN-jet workshop in Tohoku U
Prospect for the EHT: Detection of the shadow
ResultWe can estimate the size of the BH shadow within ~10-20%
low
←Pr
obab
ility
→ h
igh
Radius (𝝁𝝁as)
Ground truth
SpM
~20%
Keplerian
01/27/2018 AGN-jet workshop in Tohoku U
SummarySummary• We introduce L1+TSV regularization instead of L1+TV
regularization in order to obtain high-quality images
• We simulate observations with the EHT 2017’s array for comparing the performance of two regularizations
• As a result, we found that1. We succeed image reconstructions of BH shadows with
Sparse modeling2. Restoring beam is no longer necessary due to
L1+TSV regularization3. The size of BH shadows can be estimated within ~10-
20% using the Circular Hough Transform
Appendix
01/27/2018 AGN-jet workshop in Tohoku U
01/27/2018 AGN-jet workshop in Tohoku U
Issues1. Requirement of new imaging technique
• Image: Fourier-Transform of the visibilities (gridded)
Image: 𝑰𝑰(𝒙𝒙,𝒚𝒚)
𝒙𝒙
𝒚𝒚
Visibilities: 𝑽𝑽(𝒖𝒖,𝒖𝒖)
𝒖𝒖
𝒖𝒖2-D FT
01/27/2018 AGN-jet workshop in Tohoku U
Issues: Edge-preserving regularization
Issues1. Emission structures are overbroad and overflatter
⇒ The apparent shadow size is underestimated2. Edges of structures are over-enhanced“edge-preserving” regularization
We’d like to get more beautiful
image…Model SpM image
01/27/2018 AGN-jet workshop in Tohoku U
Issues1. Requirement of new imaging technique
• Image: Fourier-Transform of the visibilities (gridded)• This equation can be written in a linear one
Visibilities𝑽𝑽(𝑴𝑴)
Observational matrix𝑭𝑭(𝑴𝑴 × 𝑵𝑵)
Image𝑰𝑰(𝑵𝑵)
𝑴𝑴 < 𝑵𝑵: ill-posed problem
01/27/2018 AGN-jet workshop in Tohoku U
Results: Image qualityImage appearance• L1+TSV images are more similar to ground truth than
L1+TV onesImage quality• L1+TSV images have higher quality than L1+TV ones
Free-fall
Ground truth
L1+TVL1+TSV
high
←Im
age
qual
ity →
low
Restoring Beam/Clean Beam
01/27/2018 AGN-jet workshop in Tohoku U
Results: Image qualityImage appearance• L1+TSV images are more similar to ground truth than
L1+TV onesImage quality• L1+TSV images have higher quality than L1+TV ones
01/27/2018 AGN-jet workshop in Tohoku U
Results: Image qualityImage appearance• L1+TSV images are more similar to ground truth than
L1+TV onesImage quality• L1+TSV images have higher quality than L1+TV ones
Keplerian
Ground truth
L1+TVL1+TSV
high
←Im
age
qual
ity →
low
Restoring Beam/Clean Beam
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