RTF Estimation Using Riemannian Geometry for Speech Enhancement in the Presence of Interferences

We address the problem of multichannel audio signal enhancement in reverberant environments with interfering sources. We propose an approach that leverages the Riemannian geometry of the spatial correlation matrices of the received signals to estimate the relative transfer function (RTF) of the desired source. Specifically, we compute the spatial correlation matrices in short-time segments, and subsequently, their Riemannian mean, which preserves shared spatial components while attenuating unshared ones. This enables an effective rejection of intermittent interference, leading to accurate RTF estimation. We experimentally show that when the proposed RTF estimation is incorporated into the Minimum Variance Distortionless Response (MVDR) beamformer, it enhances the desired signal, outperforming the MVDR beamformer that is based on standard (Euclidean) RTF estimation. These favorable experimental results are demonstrated in challenging acoustic environments including multiple strong interfering sources, noise, and reverberations.