Straight to the Source: Detecting Aggregate Objects in Astronomical Images With Proper Error Control

Abstract

The next generation of telescopes, coming online in the next decade, will acquire terabytes of image data each night. Collectively, these large images will contain billions of interesting objects, which astronomers call sources. One critical task for astronomers is to construct from the image data a detailed source catalog that gives the sky coordinates and other properties of all detected sources. The source catalog is the primary data product produced by most telescopes and serves as an important input for studies that build and test new astrophysical theories. To construct an accurate catalog, the sources must first be detected in the image. A variety of effective source detection algorithms exist in the astronomical literature, but few, if any, provide rigorous statistical control of error rates. A variety of multiple testing procedures exist in the statistical literature that can provide rigorous error control over pixelwise errors, but these do not provide control over errors at the level of sources, which is what astronomers need. In this article, we propose a technique that is effective at source detection while providing rigorous control on sourcewise error rates. We demonstrate our approach with data from the Chandra X-ray Observatory Satellite. Our method is competitive with existing astronomical methods, even finding two new sources that were missed by previous studies, while providing stronger performance guarantees and without requiring costly follow up studies that are commonly required with current techniques.

KEY WORDS:

• Astrostatistics
• Blind source detection
• Multiple testing

Acknowledgments

This work is supported by National Science Foundation (NSF) grants 486560 and DMS0806009, National Institute of Health (NIH) grant 1R01NS047493, National Aeronautics and Space Administration (NASA) grant NNX07AH61G and the Bruce and Astrid McWilliams Center for Cosmology. The authors would like to thank Arthur Kosowsky and Neelima Seghal for the Atacama Cosmology Telescope data, Peter Freeman for his help with the Chandra X-ray telescope data and simulations, and the referees and AE for their insightful comments.

Notes

Note that repeated observations are planned for all these surveys. While this reduces the error rate, it does not eliminate the problem, especially as interest tends to focus on the deepest objects, which are the least reliably detected.

For a given (interior) pixel, we call the eight pixels surrounding it contiguous pixels to the original pixel.

Note that in our definition two overlapping sources will be treated as one “theoretical” source. This is a common simplifying assumption in many source detection algorithms. Since sources are sparse on the sky, this is unlikely; however, there are post-processing methods that can be employed to disambiguate overlapping sources. SExtractor has one such disambiguation algorithm built in to the software.

The background is estimated using the median of the data after trimming pixels that are more than five IQR from the center of the data. Since the vast majority of pixels are background, the estimate is robust to the amount of trimming.

Algorithm: Simulating a Confidence Superset for Filtered Data in Section 6.

Figure 5 Left: The galaxy clusters we want to detect. In practice these will be obscured by confounding radio signals. Middle: The Wiener filtered image which combines information from three different frequencies in an attempt to pick out the signal from the galaxy clusters while eliminating the confounding signals. This filter has introduced a nonconstant background to the image. Right: The MSD image calculated from the Wiener filtered image recovers most of the sources we are trying to detect while getting rid of most of the background variation. Data courtesy of Sehgal et al. (2007).

When the region is compact and symmetric, the third integral equal continues to hold while the first two hold to good approximation for small h.