Speech Denoising Using Transform Domains in the Presence of Impulsive and Gaussian Noises

The speech denoising problem in the presence of mixed impulsive and Gaussian noises is investigated by exploiting transform domains. To that end, the proposed noise suppression scheme is a cascaded form consisting of an impulsive noise suppression module and a Gaussian noise suppression module. For the impulsive noise reduction subsystem, in this paper, the noise is sparsely represented by the time domain, whereas short-time Fourier transform, wavelet transform, and wavelet synchrosqueezed transform are studied to provide sparse representations for the speech. By utilizing the transform domains, the speech recovery and the impulsive noise suppression are simultaneously achieved under an optimization framework. Subsequently, the alternating direction method of multipliers is used to solve 1-norm constrained optimization. In the Gaussian noise reduction subsystem, the Gaussian noise is suppressed by the famous Wiener filter in the transform domains as well. Numerical studies, including simulations and real data analysis, demonstrate the superior performance of the proposed scheme.