FAST-MEPSA: an optimised and faster version of peak detection algorithm MEPSA

We present FAST-MEPSA, an optimised version of the MEPSA algorithm developed to detect peaks in uniformly sampled time series affected by uncorrelated Gaussian noise. Although originally conceived for the analysis of gamma-ray burst (GRB) light curves (LCs), MEPSA can be readily applied to other transient phenomena. The algorithm scans the input data by applying a set of 39 predefined patterns across multiple timescales. While robust and effective, its computational cost becomes significant at large re-binning factors. To address this, FAST-MEPSA introduces a sparser offset-scanning strategy. In parallel, building on MEPSA’s flexibility, we introduce a 40th pattern specifically designed to recover a class of elusive peaks that are typically sub-threshold and lie on the rising edge of broader structures - often missed by the original pattern set. Both versions of FAST-MEPSA - with 39 and 40 patterns - were validated on simulated GRB LCs. Compared to MEPSA, the new implementation achieves a speed-up of nearly a factor 400 at high re-binning factors, with only a minor (~4%) reduction in the number of detected peaks. It retains the same detection efficiency while significantly lowering the false positive rate of low significance. The inclusion of the new pattern increases the recovery of previously undetected and sub-threshold peaks. These improvements make FAST-MEPSA an effective tool for large-scale analyses where a robust trade-off between speed, efficiency, and reliability is essential. The adoption of 40 patterns instead of the classical 39 is advisable when an enhanced efficiency in detecting faint events is desired. The code is made publicly available.

💡 Research Summary

The paper introduces FAST‑MEPSA, an optimized implementation of the Multiple Excess Peak Search Algorithm (MEPSA) originally designed for detecting peaks in uniformly sampled time series dominated by uncorrelated Gaussian noise. While MEPSA has been widely used for gamma‑ray burst (GRB) light‑curve analysis, its computational cost grows rapidly with the maximum re‑binning factor (Freb_max), scaling roughly as the cube of the re‑binning factor. This makes large‑scale searches, especially those requiring high re‑binning values, prohibitively slow.

FAST‑MEPSA tackles this problem with two complementary strategies. First, the progression of the re‑binning factor is altered: for the first ten steps the factor increases linearly (Freb = n for 1 ≤ n ≤ 10), after which it follows a quadratic law (Freb = ½ n² − 9 n + 50). This ensures continuity at the transition and yields a sparser sampling of re‑binned light curves at high factors without sacrificing sensitivity. Second, the set of possible offsets (starting points) for each re‑binned series is reduced. The step size K is defined as the smallest integer ≥ Freb/10, and offsets are generated recursively as O₀ = 0, O_{i+1} = O_i + K. Consequently, all offsets are examined for Freb ≤ 10, while for larger factors only every K‑th offset is scanned. Together, these modifications lower the algorithmic complexity from O(Freb³) to approximately O(Freb²), delivering a speed‑up of about 400× even when Freb_max = 512. Measured runtimes on simulated GRB light curves (Group 3) drop from ~412 s (original MEPSA, 39 patterns) to ~1 s for FAST‑MEPSA, regardless of whether 39 or 40 patterns are used.

In addition to the speed improvement, the authors extend the pattern library from 39 to 40 predefined templates. Analysis of previous MEPSA applications revealed that roughly 10 % of visually identified pulses were missed, most of them located on the rising edge of broader structures and possessing sub‑threshold signal‑to‑noise ratios (SNR). The new 40th pattern is specifically tuned to capture such early‑rise, low‑SNR peaks by adjusting the number of left‑hand bins and thresholds. When incorporated, this pattern markedly increases recovery of peaks with 4 ≤ SNR < 5, while only modestly affecting overall detection efficiency (a reduction of ~3–4 % compared to the original 39‑pattern version).

Performance is evaluated on three simulated data sets. Group 1 (300 light curves with Poisson‑derived Gaussian noise) and Group 2 (100 light curves with pure Gaussian background) contain no real peaks, allowing measurement of false‑positive (FP) rates. FAST‑MEPSA reduces FP counts from 56 to 13 (77 % reduction) with 39 patterns and from 75 to 37 (50 % reduction) with 40 patterns. The 40th pattern contributes the highest FP fraction, but all FPs lie in the SNR range 3–5, suggesting that a simple post‑filter (e.g., SNR > 5) can eliminate them.

Group 3 (150 light curves populated with Fast‑Rise Exponential‑Decay pulses spanning a wide SNR range) is used to assess true‑positive (TP) recovery. For peaks with SNR ≥ 5, FAST‑MEPSA detects 4 % fewer peaks than MEPSA when using 39 patterns and 3 % fewer with 40 patterns—an acceptable trade‑off given the massive speed gain. In the sub‑threshold regime (4 ≤ SNR < 5), the 40th pattern recovers a substantially larger fraction of peaks than any of the original patterns, confirming its intended purpose.

The paper also discusses practical data‑handling requirements: background subtraction must be accurate, and the Gaussian approximation to Poisson noise holds only when counts per bin are sufficiently high. If this condition is not met, users should re‑bin to increase counts or raise the SNR detection threshold; otherwise alternative algorithms designed for low‑count Poisson data are recommended.

All code and pattern definitions are released publicly (https://www.fe.infn.it/u/guidorzi/new_guidorzi_files/code.html), enabling reproducibility. Users can choose among four configurations: MEPSA or FAST‑MEPSA combined with either the 39‑pattern or 40‑pattern set. The authors advocate FAST‑MEPSA for large‑scale GRB analyses (e.g., Fermi/GBM, Swift/BAT) and for searches of sub‑threshold events coincident with gravitational‑wave triggers, where both speed and sensitivity to faint signals are critical.

In summary, FAST‑MEPSA preserves the robust statistical foundation of the original MEPSA while dramatically reducing computational demands and enhancing detection of weak, early‑rise peaks through an additional pattern. This makes it a highly practical tool for contemporary time‑domain astrophysics, where massive data volumes and the need to capture faint transients are increasingly common.