DEFINING REGIONS THAT CONTAIN COMPLEX ASTRONOMICAL STRUCTURES
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- Wiktoria Kamińska
- 4 lat temu
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1 KATY MCKEOUGH XIAO-LI MENG, VINAY KASHYAP, ANETA SIEMIGINOWSKA, DAVID VAN DYK, SHIHAO YANG, LUIS CAMPOS, DEFINING REGIONS THAT CONTAIN COMPLEX ASTRONOMICAL STRUCTURES
2 INTRODUCTION SCIENTIFIC MOTIVATION We are interested in defining an outline around extragalactic jets coming from quasars at high redshift (z>2.1) in X-ray images Defining this boundary is important for accurate luminosity and flux calculations. Jet Detecting jets is difficult because they are diffuse sources (no edges, or center) and dim compared to the quasar. Images of high redshift jets are of low resolution and few X-ray photons PKS NASA/CXC/A.Siemiginowska(CfA)/ J.Bechtold(U.Arizona) Quasar
3 BACKGROUND OBSERVATIONAL DATA Chandra X-ray Observatory - ACIS 64 x 64 or 128 x 128 pixel image centered on quasar High to intermediate redshift (2.10 < z< 4.72) Radio X-Ray
4 BACKGROUND REGION OF INTEREST Region of Interest (ROI) - region containing the jet or a partition of the jet (e.g. node or lobe) Previous work tests whether or not a jet exists in a predefined ROI (McKeough et al. 2016, Stein et al. 2015) Radio X-Ray
5 GOAL GOAL Define a probabilistic ROI around a diffuse source as a postprocessing step to LIRA.
6 LIRA LOW COUNT IMAGE RECONSTRUCTION AND ANALYSIS (LIRA) X-Ray LIRA Avg Baseline Deconvolve PSF + Extract Baseline
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sha1_base64="qo229b8guaoujuldujk5h3asijq=">aaacahicbvdlssnafl2pr1pfurcu3awwqvblugrdft24rgaf0kzhmp20gznjmjkijxtjr7hxoyhbp8odf+o0zujbd1w4c869zl0nsdht2ng+rcls8srqwng9tlg5tb1j7+41vzxkqhsk5rfsb1hrzila0exz2k4kxslgtbu83ez81iovisxrvr4l1bn4elgqeayn5nshxcugavvnvso6q/njtff17bjtcazai8tnsrly1h37q9upsspopanhsnvcj9fehqvmhnnxqzsqmmdygae0y2iebvvenj1gji6n0kdhle1fgk3v3xmzfkqnrga6bdzdne9nxp+8tqrdky9juzjqgphzr2hkky7rja3uz5iszuegyckz2rwrizayajnzyytgzp+8sjrviutu3lulcu06j6mih3aej+dcjdtgfurqaajjeizxeloerbfr3fqytrasfgyf/sd6/agfajun</latexit> ESTABLISH MODEL LIKELIHOOD q ij Z, ±, 2 ± Normal(, 2 )I zij = 1 + Normal( +, 2 +)I zij =+1 We are given observation Y from which we draw the LIRA output: Y We want to assign each pixel to either the background (-1) or the ROI (+1): Each pixel assignment will have its own average intensity:, + We suspect the variance of the source will be greater than the background: 2, 2 +
8 ESTABLISH MODEL 2D ISING PRIOR Inverse temperature: Higher induces more correlation between pixels Partition function: Z( ) Estimated via Beale (1996) assuming periodic structure Commonly used in modeling ferromagnetism. Induces spatial correlation; adjacent pixels will tend to have the same assignment.
9 PROBABILITY MAP & BOUNDARY ESTIMATE ISING-LIRA ITERATIONS 1. Get many posterior draws from LIRA 2. Apply Ising step to each LIRA draw 3. Average across LIRA-Ising iterations to get probability map
10 PROBABILITY MAP & BOUNDARY ESTIMATE PROBABILITY MAP Probability each pixel is a member of the ROI:
11 <latexit sha1_base64="cq0c3y5+jiqvg2vxpwiu5kvg6y8=">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</latexit> <latexit sha1_base64="cq0c3y5+jiqvg2vxpwiu5kvg6y8=">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</latexit> <latexit sha1_base64="cq0c3y5+jiqvg2vxpwiu5kvg6y8=">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</latexit> <latexit sha1_base64="cq0c3y5+jiqvg2vxpwiu5kvg6y8=">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</latexit> PROBABILITY MAP & BOUNDARY ESTIMATE LOCATION PROBABILITY Think about location as a random variable P (z ij =1 )! P (z =1 l =(i, j), ) Transform to probability ROI Pis in location (i,j)! P (l =(i, j) z = 1) = P (z =1 l =(i, j)) P P (z =1 l =(i, j)) ij
12 PROBABILITY MAP & BOUNDARY ESTIMATE LOCATION PROBABILITY - CREDIBLE INTERVALS CI
13 PROBABILITY MAP & BOUNDARY ESTIMATE DROPPING POINT Dropping Point - The point where the ROI becomes indistinguishable from the background Can be defined as a change point in the ordered CDF of the location
14 PROBABILITY MAP & BOUNDARY ESTIMATE ORDERED LOCATION CDF
15 PROBABILITY MAP & BOUNDARY ESTIMATE FINDING DROPPING POINT
16 PROBABILITY MAP & BOUNDARY ESTIMATE FINDING DROPPING POINT
17 PROBABILITY MAP & BOUNDARY ESTIMATE DROPPING POINT
18 PROBABILITY MAP & BOUNDARY ESTIMATE DROPPING POINT - BOUNDARY ESTIMATE ~ 40%
19 RESULTS 0
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sha1_base64="4p2grmwtspjcgqtvluwi9h1xp9y=">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</latexit> <latexit sha1_base64="4p2grmwtspjcgqtvluwi9h1xp9y=">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</latexit> <latexit sha1_base64="4p2grmwtspjcgqtvluwi9h1xp9y=">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</latexit> MODEL COMPATIBILITY Joint Model Multi-Step Process P J (,z Y ) / f(y,z) J (,z) P S (,z Y ) = P S1 ( Y )P S2 (z ) / f(y ) S1 ( ) P S 2 ( z) S2 (z) P S2 ( )
21 REFERENCES REFERENCES McKeough et al., Detecting Relativistic X-ray Jets in High-Redshift Quasars, The Astrophysical Journal (2016) Stein et al., Detecting Unspecified Structure in Low-Count Images, The Astrophysical Journal (2017) Connors & van Dyk, How To Win With Non-Gaussian Data: Poisson Goodness-of-Fit, SCMA IV (2007) Esch et al., An Image Restoration Technique with Error Estimates, The Astrophysical Journal (2004) Beale, Exact Distribution of Energy in the Two-Dimensional Ising Model, Physical Review Letters (1996) Swendsen & Wang, Nonuniversal Critical Dynamics in Monte Carlo Simulations, Physical Review Letters (1987) MacKay, D. (2004). Information theory, inference, and learning algorithms (Reprinted with corrections. ed.). Cambridge, UK ; New York: Cambridge University Press.
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