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The analysis of seismic events recorded by NASA's InSight seismometer remains challenging, given their commonly low magnitudes and large epicentral distances, and concurrently, strongly varying background noise. These factors collectively result in low signal-to-noise ratios (SNR) across most event recordings. We use a deep learning denoising approach to mitigate the noise contamination, aiming to enhance the data analysis and the seismic event catalogue. Our systematic tests demonstrate that denoising performs comparable to fine-tuned bandpass filtering at high SNRs, but clearly outperforms it at low SNRs with respect to accurate waveform and amplitude retrieval, as well as onset picking. We review the denoised waveform data of all 98 low-frequency events in the Marsquake Service catalogue version 14, and improve their location when possible through the identification of phase picks and backazimuths, while ensuring consistency with the raw data. We demonstrate that several event waveforms can be explained by marsquake doublets—two similarly strong quakes in spatio-temporal proximity that result in overlapping waveforms at InSight—and we locate them in Cerberus Fossae (CF). Additionally, we identify and investigate aftershocks and an event sequence consisting of numerous relatively high magnitude marsquakes occurring within hours at epicentral distances beyond CF. As a result of this review and interpretation, we extend the catalogue in event numbers (⁠|$+$| 8 per cent), in events with epicentral distances and magnitudes (⁠|$+$| 50 per cent), and events with backazimuths and a resulting full locations (⁠|$+$| 46 per cent), leading to a more comprehensive description of Martian seismicity. [ABSTRACT FROM AUTHOR]