Underdetermined Sound Source Separation Using Power Spectrum Density Estimated by Combination of Directivity Gain

Abstract

A method for separating underdetermined sound sources based on a novel power spectral density (PSD) estimation is proposed. The method enables up to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -1)+1 sources to be separated when we use a microphone array of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> sensors and a Wiener post-filter calculated by the estimated PSDs. The PSD of a beamformer's output is modelled by a mixture of source PSDs multiplied by the beamformer's directivity gain in the particular angle where each source is located. Based on this model, the PSD of each sound source is estimated from the PSD of multiple fixed beamformers' outputs using the difference in the combination of directivity gains. Simulation results proved that the proposed method effectively separated up to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -1)+1 sound sources if the fixed beamformers were appropriately selected. Experiments were also conducted in a reverberant chamber to ensure the proposed method was also effective in practical use.