Time-frequency fading algorithms based on Gabor multipliers

This paper addresses the problem of suppressing or attenuating time-frequency localized sources from audio signals, using only the knowledge of their time-frequency localization property. This problem, termed time-frequency fading, is formulated as a quadratic optimization problem in the signal domain, with data fidelity and penalization terms in the time-frequency plane. This allows the time-frequency coefficients of the estimated signal to be closed to the time-frequency coefficients of the observed signal outside the support of the perturbation while at the same time having a reduced energy inside the support of the perturbation. A closed-form solution is obtained that may be written in terms of Gabor multipliers, i.e. linear operators defined by pointwise multiplication in the time-frequency space. This approach, combined with efficient low-rank approximation algorithms and a suitable heuristic for hyperparameter selection, is able to efficiently process realistic signals. The effectiveness of the proposed approach is demonstrated on several audio signals where perturbations are filtered out while leading to good signal reconstruction quality.