Design of optimal wavelets for detecting impulse noise in speech

Removal of impulse noise from speech in the wavelet domain has been found to be very effective due to the multi-resolution property of the wavelet transform and the ease of removing the impulses in that domain. A critical factor that affects the performance of the impulse-removal system is the effectiveness of the impulse detection algorithm. To this end, we propose a new method for designing orthogonal wavelets that are optimized for detecting impulse noise in speech. In the method, the characteristics of the impulse noise and the underlying speech signal are taken into account and a convex optimization problem is formulated for deriving the optimal wavelet for a given support size. Performance comparison with other well-known wavelets show that the wavelets designed using the proposed method have much better impulse detection properties.