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Proper image subtraction—optimal transient detection, photometry, and hypothesis testing

Zackay, Barak and Ofek, Eran O. and Gal-Yam, Avishay (2016) Proper image subtraction—optimal transient detection, photometry, and hypothesis testing. Astrophysical Journal, 830 (1). Art. No. 27. ISSN 1538-4357.

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Transient detection and flux measurement via image subtraction stand at the base of time domain astronomy. Due to the varying seeing conditions, the image subtraction process is non-trivial, and existing solutions suffer from a variety of problems. Starting from basic statistical principles, we develop the optimal statistic for transient detection, flux measurement, and any image-difference hypothesis testing. We derive a closed-form statistic that: (1) is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise, (2) is numerically stable, (3) for accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts, (4) allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance, (5) has uncorrelated white noise, (6) is a sufficient statistic for any further statistical test on the difference image, and, in particular, allows us to distinguish particle hits and other image artifacts from real transients, (7) is symmetric to the exchange of the new and reference images, (8) is at least an order of magnitude faster to compute than some popular methods, and (9) is straightforward to implement. Furthermore, we present extensions of this method that make it resilient to registration errors, color-refraction errors, and any noise source that can be modeled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay & Ofek. We demonstrate this method on simulated data and real observations from the PTF data release 2. We provide an implementation of this algorithm in MATLAB and Python.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ofek, Eran O.0000-0002-6786-8774
Gal-Yam, Avishay0000-0002-3653-5598
Additional Information:© 2016 The American Astronomical Society. Received 2016 January 11; revised 2016 May 23; accepted 2016 June 15; published 2016 October 4. We thank Ora Zackay, Zeljko Ivesic, Robert Lupton, and Assaf Horesh for many discussions. This paper is based on observations obtained with the Samuel Oschin Telescope as part of the Palomar Transient Factory project, a scientific collaboration between the California Institute of Technology, Columbia University, Las Cumbres Observatory, the Lawrence Berkeley National Laboratory, the National Energy Research Scientific Computing Center, the University of Oxford, and the Weizmann Institute of Science. B.Z. is grateful for receiving the Clore fellowship. E.O.O. is incumbent of the Arye Dissentshik career development chair and is grateful for support by grants from the Willner Family Leadership Institute Ilan Gluzman (Secaucus NJ), Israel Science Foundation, Minerva, Weizmann-UK, and the I-Core program by the Israeli Committee for Planning and Budgeting and the Israel Science Foundation (ISF). A.G. acknowledges support from the I-Core program "The Quantum universe," as well as from the Kimmel Award.
Group:Palomar Transient Factory
Funding AgencyGrant Number
Weizmann Institute of ScienceUNSPECIFIED
Willner Family Leadership Institute Ilan GluzmanUNSPECIFIED
Israel Science FoundationUNSPECIFIED
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
Subject Keywords:gravitational lensing: micro – methods: data analysis – methods: statistical – surveys – techniques: image processing – techniques: photometric
Issue or Number:1
Record Number:CaltechAUTHORS:20190529-081531406
Persistent URL:
Official Citation:Barak Zackay et al 2016 ApJ 830 27
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95843
Deposited By: Tony Diaz
Deposited On:30 May 2019 21:35
Last Modified:03 Oct 2019 21:17

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