direct imaging and feature extraction of bh shadows with ... · with the eht kazuki kuramochi...

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


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


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


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


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…


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


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


Results: Image appearance• L1+TSV images are more similar to ground truth than

L1+TV ones

Sub-KeplerianL1+TV image L1+TSV imageGround truth


Results: Image appearance• L1+TSV images are more similar to ground truth than

L1+TV ones

KeplerianL1+TV image L1+TSV imageGround truth


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


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



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



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


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



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


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


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


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




Keplerian

Ground truth

L1+TVL1+TSV

high

←Im

age

qual

ity →

low

Restoring Beam/Clean Beam

direct imaging and feature extraction of bh shadows with ... · with the eht kazuki kuramochi...

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