Speech denoising in the presence of Impulsive Noise

This work addresses speech denoising problem in the presence of impulsive noise in transform domains. The impulsive noise, in this work, is modeled by an unknown sparse vector so that it can be actively suppressed. The speech signal is sparsely represented by the wavelet domain. To achieve the simultaneous speech recovery and the noise suppression, a joint estimation is devised based on the fact they have sparse representations in different domains. To efficiently solve the problem, the alternating direction method of multipliers (ADMM) is adopted to obtain the solution. Simulation results demonstrate the superior performance of the proposed approach.