limited short baselines), but we are able to detect small scale faint emission using the method outlined here.

In the following sections, we describe our procedure in details. We improve the data quality by flattening the spectral baselines (section \[sec:flattening\]). We use the source-finding application SoFiA (Serra et al. 2015) to extract all signal exceeding 4 $\sigma$. After removing all bright, reliable detections (section \[sec:scfinding\]), we are left with “noise” peaks which we analyse in order to detect a statistical signal. We perform a series of careful tests to examine the robustness of the accumulative signal against various data reduction artefacts (section \[sec:testing\]).

Flattening the spectral baselines {#sec:flattening}
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In order to improve the quality of the [[H]{}[<span style="font-variant:small-caps;">i</span> ]{}]{}data cubes we fit second-order polynomial functions in moving windows along each line of sight. This allows us to obtain global functions describing the shape of the spectral baselines without specifying their functional form. In practice, we convolve each spectrum with the Savitzky-Golay filter (S-G, Savitzky & Golay 1964), an analytical solution for the local fitting process. We adopt a S-G filter with a half width of 70 channels (840 km/s), wider than the velocity width of all the galaxies in 