Optimal Matched Filter in the Low-number Count Poisson Noise Regime and Implications for X-Ray Source Detection
Optimal Matched Filter in the Low-number Count Poisson Noise Regime and Implications for X-Ray Source Detection
复制标题
低数泊松噪声域中的最佳匹配滤波器及其对 X 射线源检测的影响
DOI：
10.3847/1538-3881/aab265
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
B. Zackay
中科院分区：
文献类型：
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作者：
E. Ofek;B. Zackay
模板的检测（例如，在天体物理学中，低计数泊松噪声中的噪声源（例如，噪声源）是一个常见的问题。例子包括X射线图像中的源探测，γ射线，紫外线，中微子，以及星系团和恒星流的搜索。然而，X射线相关文献中的解决方案在某些情况下由于相当大的因素而次优。利用Neyman-Pearson引理，我们推导了泊松噪声存在下的模板检测的最优统计量。我们证明，对于已知的模板形状（例如，点源），该方法提供了更高的完整性，对于一个固定的虚警概率值，与过滤的图像与点扩散函数（PSF）。反过来，我们发现通过PSF滤波比使用墨西哥帽小波（wavdetect使用）滤波图像更好。对于某些背景水平，我们的方法比流行的墨西哥帽小波滤波将源检测的灵敏度提高了两倍以上。这种滤波技术也可以用于快速PSF测光和耀斑检测;它是高效和简单的实施。我们提供了一个在MATLAB中的实现。开发一个完整的代码，工作在真实的数据，包括复杂的背景减法和PSF的变化，被推迟到未来的出版。
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.