Optimal Matched Filter in the Low-number Count Poisson Noise Regime and Implications for X-Ray Source Detection

• Published in: The Astronomical journal Vol. 155; no. 4; pp. 169 - 176
• Main Authors: Ofek, Eran O., Zackay, Barak
• Format: Journal Article
• Language: English
• Published: Madison The American Astronomical Society 01.04.2018; IOP Publishing
• Subjects: Astronomy; ASTROPHYSICS; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; Baseline studies; COMPARATIVE EVALUATIONS; COSMIC X-RAY SOURCES; False alarms; FILTERS; Galaxies; GALAXY CLUSTERS; Image detection; Image filters; IMAGE PROCESSING; Matched filters; methods: statistical; NEUTRINOS; NOISE; PHOTOMETRY; POINT SOURCES; Point spread functions; SENSITIVITY; Star clusters; STATISTICS; Subtraction; techniques: image processing; techniques: photometric; Wavelet analysis; X RADIATION; X ray sources; X-RAY DETECTION
• ISSN: 0004-6256; 1538-3881; 1538-3881
• DOI: 10.3847/1538-3881/aab265

Detection of templates (e.g., sources) embedded in low-number count Poisson noise is a common problem in astrophysics. Examples include source detection in X-ray images, γ-rays, UV, neutrinos, and search for clusters of galaxies and stellar streams. However, the solutions in the X-ray-related literature are sub-optimal in some cases by considerable factors. Using the lemma of Neyman-Pearson, we derive the optimal statistics for template detection in the presence of Poisson noise. We demonstrate that, for known template shape (e.g., point sources), this method provides higher completeness, for a fixed false-alarm probability value, compared with filtering the image with the point-spread function (PSF). In turn, we find that filtering by the PSF is better than filtering the image using the Mexican-hat wavelet (used by wavdetect). For some background levels, our method improves the sensitivity of source detection by more than a factor of two over the popular Mexican-hat wavelet filtering. This filtering technique can also be used for fast PSF photometry and flare detection; it is efficient and straightforward to implement. We provide an implementation in MATLAB. The development of a complete code that works on real data, including the complexities of background subtraction and PSF variations, is deferred for future publication.