3 years ago

Matched filter in the low-number count Poisson noise regime: an efficient and effective implementation.

Paola Andreani, Roberto Vio

The matched filter (MF) is widely used to detect signals hidden within the noise. If the noise is Gaussian its performances are well-known and describable in an elegant analytical form. The treatment of non-Gaussian noises is often cumbersome as in most of the cases there is no analytical framework. This is true also for Poisson noise which, especially in the low-number count regime, presents the additional difficulty to be discrete. For this reason, in the past methods based on heuristic or semi-heuristic arguments have been proposed. Recently an analytical form of the MF has been obtained but in the proposed implementation the computation of the probability of false detection or false alarm (PFA) is based on numerical simulations. This is an inefficient and time consuming approach. Here we present an effective method to compute the PFA based on the saddle-point approximation which is fast, able to provide excellent results and easy to implement. Theoretical arguments are provided as well the results of some numerical experiments.

Publisher URL: http://arxiv.org/abs/1801.02859

DOI: arXiv:1801.02859v1

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