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A transient is an abrupt or impulsive sound followed by decaying oscillations, e.g., keyboard typing and door knocking. Such sounds often arise as interference in everyday applications, e.g., hearing aids, hands-free accessories, mobile phones, and conference-room devices. In this paper, we present an algorithm for single-channel transient interference suppression. The main component of the proposed algorithm is the estimation of the spectral variance of the interference. We propose a statistical model of the transient interference and combine it with non-local filtering. We exploit the unique spectral structure of the transients along with their impulsive temporal nature to distinct them from speech. A particular attention is given to handling both short- and long-duration transients. Experimental results show that the proposed algorithm enables significant transient suppression for a variety of transient types.