Efficient Alternatives to the Ephraim and Malah Suppression Rule for Audio Signal Enhancement
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Efficient Alternatives to the Ephraim and Malah Suppression Rule for Audio Signal Enhancement Patrick J. Wolfe Signal Processing Group, Department of Engineering, University of Cambridge, CB2 1PZ Cambridge, UK Email: [email protected]
Simon J. Godsill Signal Processing Group, Department of Engineering, University of Cambridge, CB2 1PZ Cambridge, UK Email: [email protected] Received 31 May 2002 and in revised form 20 February 2003 Audio signal enhancement often involves the application of a time-varying filter, or suppression rule, to the frequency-domain transform of a corrupted signal. Here we address suppression rules derived under a Gaussian model and interpret them as spectral estimators in a Bayesian statistical framework. With regard to the optimal spectral amplitude estimator of Ephraim and Malah, we show that under the same modelling assumptions, alternative methods of Bayesian estimation lead to much simpler suppression rules exhibiting similarly effective behaviour. We derive three of such rules and demonstrate that, in addition to permitting a more straightforward implementation, they yield a more intuitive interpretation of the Ephraim and Malah solution. Keywords and phrases: noise reduction, speech enhancement, Bayesian estimation.
1.
INTRODUCTION
Herein we address an important issue in audio signal processing for multimedia communications, that of broadband noise reduction for audio signals via statistical modelling of their spectral components. Due to its ubiquity in applications of this nature, we concentrate on short-time spectral attenuation, a popular method of broadband noise reduction in which a time-varying filter, or suppression rule, is applied to the frequency-domain transform of a corrupted signal. We first address existing suppression rules derived under a Gaussian statistical model and interpret them in a Bayesian framework. We then employ the same model and framework to derive three new suppression rules exhibiting similarly effective behaviour, preliminary details of which may also be found in [1]. These derivations lead in turn to a more intuitive means of understanding the behaviour of the well-known Ephraim and Malah suppression rule [2], as well as to an extension of certain others [3, 4]. This paper is organised as follows. In the remainder of Section 1, we introduce the assumed statistical model and estimation framework, and then employ these in an alternate derivation of the minimum mean square error (MMSE) suppression rules due to Wiener [5] and Ephraim and Malah [2]. In Section 2, we derive three alternatives to the MMSE spec-
tral amplitude estimator of [2], all of which may be formulated as suppression rules. Finally, in Section 3, we investigate the behaviour of these solutions and compare their performance to that of the Ephraim and Malah suppression rule. Throughout the ensuing discussion, we consider—for simplicity of notation and without loss of generality—the case of a single, windowed segment of audio data. To facilitate a comparison, our notation follows that of
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