Super-resolution Polarimetric Imaging of Black Holes using the

Event Horizon TelescopeMIT Haystack Observatory

Mollie Pleau Mentors: Kazunori Akiyama

Vincent Fish

The Event Horizon Telescope (EHT)● Created to image black hole shadow of Sgr A* (55μas, 8kpc,

4x106M☉

) and M87 (36μas, 16 Mpc, 6.3x109 M☉

)● A global effort: seven millimeter/submillimeter sites

Objectives include:

● Testing general relativity

● Understanding jet generation and collimation in galaxies

● Understanding accretion around black holes

Increasing Image Fidelity

● Resolution goes as λ ⁄B ● As more telescopes are added to the

EHT array, we can increase our image fidelity by increasing UV coverage

● Each measurement is called a visibility, and each is mathematically a Fourier Transform:

EHT UV Coverage (M87)

A larger baseline increases resolution, and more telescopes increases sensitivity

http://inspirehep.net/record/1292771/plots

(Honma et. al 2014)

Polarimetric Imaging● Synchrotron emission is inherently polarized● Polarimetric imaging can help characterize the magnetic field

○ Stokes parameters: We image Q and U-map (linear polarization) as well as P-map (Q+iU)

● We require super-resolution (i.e. structure finer than the beam size can

be reproduced) to accurately reconstruct linear polarimetric images

The Standard Imaging Technique

● CLEAN (Jan Högbom 1974)○ Backward imaging technique, i.e. Fourier transform visibilities first to

make “dirty map”○ Designed to image point sources (extensions exist to image extended

structure)

Cons ● User dependent● Dirty beam (point spread function) is not conducive to producing

super-resolution results● Assumes that image can be broken down into many point sources

In order to obtain a high fidelity reconstructed image, we must employ statistical imaging methods

Sparse Modeling● Forward imaging technique: works in visibility domain

○ Tries to reconstruct images for which there are more pixels than data points

○ Based on idea of sparsity, i.e. that the majority of pixels have a value of 0

○ There are thousands of images that mathematically fit the data wellThough these images technically fit the data, they are overfitted

○ Least squares fit with penalties (regularizers) to try to narrow down amount of images that are a good fit

Example● A technique used in Magnetic Resonance Imaging (MRI)● Same philosophy as CLEAN: reconstructing a “sparse” image

w/o Sparse Modeling with Sparse Modeling

MRI image of the cerebral blood vessel

Regularizers● We impart regularization factors to solve images

○ We must determine what type of regularization factor and how much of this factor to impart on the data

Sparsity Regularization Less overfitting

Regularizers:

● L1-norm: Favors a sparse solution.

TV-norm (Total Variation): Favors a smoother solution.

χ2 (With Penalties)

Cross ValidationA statistical method used to assess how well a model will generalize to an independent data set

The role of CV:

● To help determine how tune parameters, i.e. how much of each regularizer to use

● Used to train data in order to figure out which weights of the regularizer work best

https://dfzljdn9uc3pi.cloudfront.net/2015/1251/1/fig-5-1x.jpg

We select the smallest value of 2 from the training data set compared to the validating data set

L1

TV(Higher weight)

(Higher weight)

Methods ● We use data from simulated observations from EHT for M87● Employ different methods and solvers to image data● Test image reconstruction for five different models● Determine which L1+TV weights optimize each image● Check results quantitatively

Forward Jet Counter Jet

Images

Forward Jet Model

TARGET CLEAN L1&TVPure-L1 Pure-TV

Images

Counter Jet Model

TARGET CLEAN L1&TVPure-L1 Pure-TV

FidelityModel

L1+TV

CLEAN

5 uas 15 uas 25uas

Super Resolution

Sparse Modeling

CLEAN fails to reconstruct Electric Vector Position Angles (EVPA), fractional polarization, and the event horizon shadow, whereas L1&TV reconstructs them well

Conclusions● We find that sparse modeling can reconstruct higher

fidelity images than CLEAN by a factor of 10○ At finer beam sizes, sparse modeling produces

better images● For polarimetric imaging, we must use L1+TV● Whether we regularize P-map or (Q,U)-maps

separately, our results are similar to within a few percent

A special thanks to:My mentors: Kazunori Akiyama and Vincent Fish

REU Lecture Series speakers

National Science Foundation

The entire MIT Haystack Staff and summer group