Quadratic approach for single-channel noise reduction

Abstract

AbstractIn this paper, we introduce a quadratic approach for single-channel noise reduction. The desired signal magnitude is estimated by applying a linear filter to a modified version of the observations’ vector. The modified version is constructed from a Kronecker product of the observations’ vector with its complex conjugate. The estimated signal magnitude is multiplied by a complex exponential whose phase is obtained using a conventional linear filtering approach. We focus on the linear and quadratic maximum signal-to-noise ratio (SNR) filters and demonstrate that the quadratic filter is superior in terms of subband SNR gains. In addition, in the context of speech enhancement, we show that the quadratic filter is ideally preferable in terms of perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI) scores. The advantages, compared to the conventional linear filtering approach, are particularly significant for low input SNRs, at the expanse of a higher computational complexity. The results are verified in practical scenarios with nonstationary noise and in comparison to well-known speech enhancement methods. We demonstrate that the quadratic maximum SNR filter may be superior, depending on the nonstationary noise type.