Filtering Out Time-Frequency Areas Using Gabor Multipliers

We address the problem of filtering out localized time-frequency components in signals. The problem is formulated as a minimization of a suitable quadratic form, that involves a data fidelity term on the short-time Fourier transform outside the support of the undesired component, and an energy pe- nalization term inside the support. The minimization yields a linear system whose solution can be expressed in closed form using Gabor multipliers. We provide an analysis of the solution and its approximation by truncated eigenvalue expansion, and illustrate its performance on synthetic mixtures of audio signals. The proposed approach outperforms approaches that are routinely used in applications.