Beyond the Narrowband Approximation: Wideband Convex Methods for Under-Determined Reverberant Audio Source Separation

We consider the problem of extracting the source signals from an under-determined convolutive mixture assuming known mixing filters. State-of-the-art methods operate in the time-frequency domain and rely on narrowband approximation of the convolutive mixing process by complex-valued multiplication in each frequency bin. The source signals are then estimated by minimizing either a mixture fitting cost or a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ℓ</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> source sparsity cost, under possible constraints on the number of active sources. In this paper, we define a wideband ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> mixture fitting cost circumventing the above approximation and investigate the use of a ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,2</sub> mixed-norm cost promoting disjointness of the source time-frequency representations. We design a family of convex functionals combining these costs and derive suitable optimization algorithms. Experiments indicate that the proposed wideband methods result in a signal-to-distortion ratio improvement of 2 to 5 dB compared to the state-of-the-art on reverberant speech mixtures.