Noise Reduction with Optimal Variable Span Linear Filters

Abstract

In this paper, the problem of noise reduction is addressed as a linear filtering problem in a novel way by using concepts from subspace-based enhancement methods, resulting in variable span linear filters. This is done by forming the filter coefficients as linear combinations of a number of eigenvectors stemming from a joint diagonalization of the covariance matrices of the signal of interest and the noise. The resulting filters are flexible in that it is possible to trade off distortion of the desired signal for improved noise reduction. This tradeoff is controlled by the number of eigenvectors included in forming the filter. Using these concepts, a number of different filter designs are considered, like minimum distortion, Wiener, maximum SNR, and tradeoff filters. Interestingly, all these can be expressed as special cases of variable span filters. We also derive expressions for the speech distortion and noise reduction of the various filter designs. Moreover, we consider an alternative approach, wherein the filter is designed for extracting an estimate of the noise signal, which can then be extracted from the observed signals, which is referred to as the indirect approach. Simulations demonstrate the advantages and properties of the variable span filter designs, and their potential performance gain compared to widely used speech enhancement methods.

Microphone Subset Selection for MVDR Beamformer Based Noise Reduction

“…To focus on the concept of sensor selection, we assume that the steering vector a is known. In practice, this can be estimated using source localization algorithms, e.g., [35] [36], in combination with the sensor locations, or, by calculating the generalized eigenvalue decomposition of the matrices R nn and R yy [38] [39]. For the wireless transmission model in (12), we consider the simplest wireless transmission case, where the transmission cost between each sensor and the FC is proportional to the square of their Euclidean distance [47], and we assume that the device dependent cost c (0) i = 0, ∀i.…”

Rank-1 constrained Multichannel Wiener Filter for speech recognition in noisy environments

“…This choice of µ = µ G is new in the context of rank-1 MWF. Although it has been known that linear filters are equivalent up to a scaling factor [24,27,28], the factor that specifically relates the rank-1 MWF and GEV is given here by 1 µG+λ for the first time.…”

“…MWF [20] is a Minimum Mean Square Error (MMSE) solution which allows for given noise reduction at the expense of some speech distortion. There exist other linear filter variants, such as the Speech Distortion Weighted MWF (SDW-MWF) [21,22,23] and the Variable Span (VS) linear filter [24]. The SDW-MWF involves a tradeoff parameter which tunes the speech distortion versus the noise reduction.…”

Sound Zones As An Optimal Filtering Problem

“…Although µ in (6) provides us with a handle for controlling the trade-off between speech distortion and noise suppression, we can obtain an even better control over this trade-off by essentially enforcing a low rank approximation to the clean speech covariance matrix Rs. This is the main rationale behind the variable span linear filtering (VSLF) framework [17,19] and also the principle which unifies the optimal filtering and subspace approaches to speech enhancement. To derive this, first consider the joint diagonalisation (also sometimes referred to as the generalised eigenvalue decomposition or matrix pencil) of the positive semi-definite clean speech covariance matrix Rs and positive definite noise covariance matrix Re [29, p. 106]…”

“…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]. Interestingly, the resulting sound zone control framework (VAST) has many of the existing control methods such as ACC, PM, and their variations as special cases.…”