On the Correct Estimate of the Probability of False Detection of the Matched Filter in Weak-Signal Detection Problems

Abstract

The detection reliability of weak signals is a critical issue in many astronomical contexts and may have severe consequences for determining number counts and luminosity functions, but also for optimising the use of telescope time in follow-up observations. Because of its optimal properties, one of the most popular and widely-used detection technique is the matched filter (MF). This is a linear filter designed to maximise the detectability of a signal of known structure that is buried in additive Gaussian random noise. In this work we show that in the very common situation where the number and position of the searched signals within a data sequence (e.g. an emission line in a spectrum) or an image (e.g. a point-source in an interferometric map) are unknown, this technique, when applied in its standard form, may severely underestimate the probability of false detection. This is because the correct use of the MF relies upon a-priori knowledge of the position of the signal of interest. In the absence of this information, the statistical significance of features that are actually noise is overestimated and detections claimed that are actually spurious. For this reason, we present an alternative method of computing the probability of false detection that is based on the probability density function (PDF) of the peaks of a random field. It is able to provide a correct estimate of the probability of false detection for the one-, two- and three-dimensional case. We apply this technique to a real two-dimensional interferometric map obtained with ALMA.

Accepted for publication by A&A

References in corpus (4)

• The assembly of "normal" galaxies at z=7 probed by ALMA
• ALMA constraints on the faint millimetre source number counts and their contribution to the cosmic infrared background
• On the Explicit Height Distribution and Expected Number of Local Maxima of Isotropic Gaussian Random Fields
• Matched Filters for Source Detection in the Poissonian Noise Regime

Cited by in corpus (16)

• Detecting Weak Spectral Lines in Interferometric Data through Matched Filtering
• The MUSE-Wide Survey: A first catalogue of 831 emission line galaxies
• Alma Twenty-six Arcmin^2 Survey Of Goods-s At One-millimeter (asagao): Source Catalog And Number Counts
• The CO Luminosity Density at High-z (COLDz) Survey: A Sensitive, Large Area Blind Search for Low-J CO Emission from Cold Gas in the Early Universe with the Karl G. Jansky Very Large Array
• LSDCat: Detection and cataloguing of emission-line sources in integral-field spectroscopy datacubes
• Deciphering Lyman $\alpha$ blob 1 with deep MUSE observations
• ORIGIN: Blind detection of faint emission line galaxies in MUSE datacubes
• A stellar census in globular clusters with MUSE: A spectral catalogue of emission-line sources
• To see or not to see a $z\sim 13$ galaxy, that is the question
• The correct estimate of the probability of false detection of the matched filter in the detection of weak signals. II. (Further results with application to a set of ALMA and ATCA data)
• Correct estimate of the probability of false detection of the matched filter in weak-signal detection problems. III (Peak distribution method versus the Gumbel distribution method)
• ALMA CO(2-1) observations in the XUV disk of M83
• Revisiting the Emission Line Source Detection Problem in Integral Field Spectroscopic Data
• Quantifying the detection likelihood of faint peaks in interferometric data through jackknifing: Test application on finding $z>10$ galaxy candidates
• Matched filter in the low-number count Poisson noise regime: an efficient and effective implementation
• Revisiting BD-06 1339b: A Likely False Positive Caused by Stellar Activity