On Homotopy Continuation for Speech Restoration.

In this paper, a homotopy-based method is employed for the recovery of speech recordings from missing or corrupted samples taken in a noisy environment. The model for the acquisition device is a compressed sensing scenario using Gabor frames. To recover an approximation of the speech file, we used the basis pursuit denoising method with the homotopy continuation algorithm. We tested the proposed method with various speech recordings.