Quadratic approach for single-channel noise reduction

Gal Itzhak,Israel Cohen,Jacob Benesty

doi:10.1186/s13636-020-00174-4

Abstract

In 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.

Highlights

Communications and signal processing systems are very likely to operate in adverse environments, which are characterized by the presence of background noise that might severely degrade the quality of desired signals
We present a quadratic approach for Single-channel noise reduction (SCNR) which extends the multi-frame approach suggested in [18]
), 6 Experimental results we demonstrate the noise reduction capabilities of the quadratic maximum signal-to-noise ratio (SNR) filter in the context of speech enhancement

Summary

Introduction

Communications and signal processing systems are very likely to operate in adverse environments, which are characterized by the presence of background noise that might severely degrade the quality of desired signals. Noise reduction methods are designed and applied to noisy signals with the objective of improving their quality and attenuating the background noise. Single-channel noise reduction (SCNR) methods are often implemented in physically small or low cost systems. SCNR filters are usually derived by minimizing a given distortion function between the clean signal and its estimate, or by minimizing the energy of the residual noise under some constraints. The optimal filter is derived in the chosen domain and applied to the transformed observations. The filtered observations are transformed back to the time domain using the inverse STFT

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