Objective algorithm to separate signal from noise in a Poisson-distributed pixel data set

Abstract

A statistical method to determine the background level and separate signal from background in a Poisson-distributed background data set is described. The algorithm eliminates the pixel with the highest intensity value in an iterative manner until the sample variance equals the sample mean within the estimated uncertainties. The eliminated pixels then contain signal superimposed on the background, so the integrated signal can be obtained by summation or by a simple extension by profile fitting depending on the user's preferences. Two additional steps remove `outliers' and correct for the underestimated extension of the peak area, respectively. The algorithm can be easily modified to specific needs, and an application on crystal truncation rods is presented, dealing with a sloping background.