Median Algorithm for Sector Spectra Calculation from Images Registered by the Spectral Airglow Temperature Imager

The Spectral Airglow Temperature Imager is an instrument, specially designed for investigation of the wave processes in the Mesosphere-Lower Thermosphere. In order to determine the kinematic parameters of a wave, the values of a physical quantity in different space points and their changes in the time should be known. As a result of the possibilities of the SATI instrument for space scanning, different parts of the images (sectors of spectrograms) correspond to the respective mesopause areas (where the radiation is generated). An approach is proposed for sector spectra determination from SATI images based on ordered statistics instead of meaning. Comparative results are shown.

💡 Research Summary

The paper introduces a novel data‑processing technique for the Spectral Airglow Temperature Imager (SATI), an optical instrument used to monitor temperature and emission rates in the mesopause region of the mesosphere‑lower thermosphere. Traditional SATI processing divides each circular sky image into twelve 30° sectors, determines the distance of every pixel from the image centre, and then averages the intensities of all pixels that share the same radial distance within a sector. While straightforward, this averaging approach is vulnerable to impulsive “salt‑and‑pepper” noise generated by high‑energy particles, which can bias the derived sector spectra and consequently the temperature estimates.

To mitigate this problem, the author proposes replacing the arithmetic mean with the median, i.e., an order‑statistic filter. The new algorithm proceeds as follows: after standard pre‑processing (cosmic‑ray rejection, dark‑frame correction, sub‑pixel centre localisation), each sector is defined by an arbitrary central angle θ and a sector width γ (typically 5°–40°). For every pixel belonging to a sector, the Euclidean distance p from the centre is computed and the pixel’s intensity is stored in a two‑dimensional array W(q, p), where each column p contains all intensities at that radius. Using the Visual Digital Fortran routine sortqq, each column is sorted in ascending order; the median (the middle element of the sorted list) is then taken as the representative intensity for radius p in that sector’s spectrum.

Because the median discards extreme outliers, pixels corrupted by impulsive noise do not influence the final spectrum. The author validates the method by processing SATI data with sector angles of 5°, 15°, 30°, 45°, and 60°. Results show that the temperature values derived from median‑based spectra differ from those obtained with the conventional mean by only a few kelvin at the smallest sector angle, and the discrepancy virtually disappears as the sector angle increases. Moreover, the standard deviation of the nocturnal temperature series systematically declines with larger γ, indicating improved stability. The median approach also yields smoother, denoised temperature curves when a simple temporal filter is applied to the series.

Computationally, the median method incurs a higher cost than simple averaging because sorting is O(N log N) rather than O(N). However, the number of pixels per sector is modest (a few hundred), so the additional processing time is negligible on typical ground‑based workstations. The author notes that alternative sorting algorithms (heap sort, merge sort) could be employed, and that for very small N the overhead is minimal. An extension is suggested: instead of using only the pixels at radius p, one could jointly sort the intensities at radii p‑1, p, p + 1, thereby introducing a spatial smoothing step that remains a non‑linear order‑statistic operation.

In conclusion, the median‑based sector‑spectra extraction provides a robust alternative to averaging, especially under low signal‑to‑noise conditions. It reduces the influence of impulsive noise, improves temperature precision, and retains flexibility in sector definition. Future work will explore more efficient sorting techniques, multi‑median (e.g., trimmed mean or trimean) schemes, and the impact of these statistical choices on the retrieval of atmospheric wave parameters. The author also envisions applying the same order‑statistic framework to other derived quantities such as emission rates, thereby broadening the utility of the method within the SATI data‑analysis community.