This paper presents an automatic method for simultaneous detection and elimination of impulsive noises from audio signals. The method is based on the sparse signal decomposition (SSD) with overcomplete hybrid dictionary (OHD) matrix including impulse and sinusoidal waveforms derived from discrete impulse, sine and cosine functions, and 1-norm optimization algorithm. The SSD technique decomposes an audio signal into two parts: an approximation part including the sinusoidal components; and a detail part including the impulsive and background noise components. Results show that the impulse waveforms can adequately capture clicks, pops and record scratches in audio signals meanwhile the sinusoids of the OHD matrix can effectively capture sinusoidal components. For performance comparison purpose, four restoration methods are implemented based on the representation dictionaries, median filter, and signal dependent rank order mean techniques. The methods are validated using audio signals extracted from old archive Indian and English movies and standard music database. The quality of the restored audio signals is evaluated using both subjective quality and objective quality metrics. Results show that the proposed method effectively removes impulsive noises without degrading the perceived audio quality and its intelligibility as compared to the existing restoration methods. © 2017 IEEE.