Audio restoration from multiple copies

A method for removing impulse noise from audio signals by fusing multiple copies of the same recording is introduced in this paper. The proposed algorithm exploits the fact that while in general multiple copies of a given recording are available, all sharing the same master, most degradations in audio signals are record-dependent. Our method first seeks for the optimal non-rigid alignment of the signals that is robust to the presence of sparse outliers with arbitrary magnitude. Unlike previous approaches, we simultaneously find the optimal alignment of the signals and impulsive degradation. This is obtained via continuous dynamic time warping computed solving an Eikonal equation. We propose to use our approach in the derivative domain, reconstructing the signal by solving an inverse problem that resembles the Poisson image editing technique. The proposed framework is here illustrated and tested in the restoration of old gramophone recordings showing promising results; however, it can be used in other applications where different copies of the signal of interest are available and the degradations are copy-dependent.