Optimal matched filter in the low-number count Poisson noise regime and implications for X-ray source detection

TL;DR

This paper derives the optimal detection statistic for low-count Poisson noise in astrophysical images, significantly improving source detection sensitivity over traditional methods like PSF filtering and Mexican-hat wavelets.

Contribution

It introduces a Neyman-Pearson based optimal detection method for Poisson noise, outperforming existing filtering techniques in astrophysical source detection.

Findings

Optimal detection statistic improves sensitivity by over a factor of two.

Filtering by the PSF outperforms Mexican-hat wavelet filtering.

Method is efficient, easy to implement, and applicable to various astrophysical detection tasks.

Abstract

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, gamma-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 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 wavedetect). 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 also for fast PSF photometry and flare detection, and it is efficient, as well as straight forward to implement. We provide an implementation in MATLAB.