A brief overview of speech enhancement with linear filtering

Abstract

In this paper, we provide an overview of some recently introduced principles and ideas for speech enhancement with linear filtering and explore how these are related and how they can be used in various applications. This is done in a general framework where the speech enhancement problem is stated as a signal vector estimation problem, i.e., with a filter matrix, where the estimate is obtained by means of a matrix-vector product of the filter matrix and the noisy signal vector. In this framework, minimum distortion, minimum variance distortionless response (MVDR), tradeoff, maximum signal-to-noise ratio (SNR), and Wiener filters are derived from the conventional speech enhancement approach and the recently introduced orthogonal decomposition approach. For each of the filters, we derive their properties in terms of output SNR and speech distortion. We then demonstrate how the ideas can be applied to single-and multichannel noise reduction in both the time and frequency domains as well as binaural noise reduction.

Sound Zones As An Optimal Filtering Problem

“…Fourth, and finally, speech and some noise types are highly non-stationary which means that segment-bysegment processing under a local stationarity assumption should be performed for short segments. Although a number of different approaches to speech enhancement exist based on, e.g., spectral substraction [23], statistical models [24], binary masking [25], subspace techniques [26], and non-negative matrix factorisations [27], the majority of enhancement methods can be classified as an optimal filtering approach [18] or has such an interpretation. The basic idea in the optimal filtering approach is to design an FIR filter h ∈ R M which filters out the noise and preserves the clean speech from the noisy speech signal, i.e.,ŝ…”

“…More specifically, most speech enhancement methods involve the design of an FIR filter which filters out the noise from the noisy speech input signal while simultaneously preserving the clean speech signal in the output signal. This approach to doing speech enhancement is often referred to as optimal filtering [18] and, as the title of the present paper suggests, the optimal filtering principle can actually be adopted for the design of sound zones. We recently discovered this connection and used this insight to adapt the very flexible variable span linear filtering (VSLF) framework from speech enhancement [17,19] to sound zone control [20].…”

Speech enhancement using robust estimators and rank-order statistics

“…Speech enhancement is commonly posed as an estimation problem to retrieve the magnitude spectrum of a clean speech signal from a noisy signal. There are several successful estimators for speech enhancement (Benesty et al, 2014;Hansen and Jensen, 2007). Some well known estimators are the maximum-likelihood (ML) (Loizou, 2013;McAulay and Malpass, 1980;Kim and Chang, 2000) and Bayesian estimators such as the minimum meansquared-error (MMSE) (Ephraim and Malah, 1984;Ding et al, 2004;Martin, 2005;Fodor et al, 2015;Lu and Loizou, 2011), the log-MMSE (Ephraim and Malah, 1985), and the maximum a posteriori probability (MAP) estimators (Loizou, 2013;Lotter and Vary, 2005).…”