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Enhancement of speech signals for hands-free communication systems has attracted significant research efforts in the last few decades. Still, many aspects and applications remain open and require further research. One of the important open problems is the single-channel transient noise reduction. In this paper, we present a novel approach for transient noise reduction that relies on non-local (NL) neighborhood filters. In particular, we propose an algorithm for the enhancement of a speech signal contaminated by repeating transient noise events. We assume that the time duration of each reoccurring transient event is relatively short compared to speech phonemes and model the speech source as an auto-regressive (AR) process. The proposed algorithm consists of two stages. In the first stage, we estimate the power spectral density (PSD) of the transient noise by employing a NL neighborhood filter. In the second stage, we utilize the optimally modified log spectral amplitude (OM-LSA) estimator for denoising the speech using the noise PSD estimate from the first stage. Based on a statistical model for the measurements and diffusion interpretation of NL filtering, we obtain further insight into the algorithm behavior. In particular, for given transient noise, we determine whether estimation of the noise PSD is feasible using our approach, how to properly set the algorithm parameters, and what is the expected performance of the algorithm. Experimental study shows good results in enhancing speech signals contaminated by transient noise, such as typical household noises, construction sounds, keyboard typing, and metronome clacks.