Single-channel noise reduction using unified joint diagonalization and optimal filtering

Abstract

In this paper, the important problem of single-channel noise reduction is treated from a new perspective. The problem is posed as a filtering problem based on joint diagonalization of the covariance matrices of the desired and noise signals. More specifically, the eigenvectors from the joint diagonalization corresponding to the least significant eigenvalues are used to form a filter, which effectively estimates the noise when applied to the observed signal. This estimate is then subtracted from the observed signal to form an estimate of the desired signal, i.e., the speech signal. In doing this, we consider two cases, where, respectively, no distortion and distortion are incurred on the desired signal. The former can be achieved when the covariance matrix of the desired signal is rank deficient, which is the case, for example, for voiced speech. In the latter case, the covariance matrix of the desired signal is full rank, as is the case, for example, in unvoiced speech. Here, the amount of distortion incurred is controlled via a simple, integer parameter, and the more distortion allowed, the higher the output signal-to-noise ratio (SNR). Simulations demonstrate the properties of the two solutions. In the distortionless case, the proposed filter achieves only a slightly worse output SNR, compared to the Wiener filter, along with no signal distortion. Moreover, when distortion is allowed, it is possible to achieve higher output SNRs compared to the Wiener filter. Alternatively, when a lower output SNR is accepted, a filter with less signal distortion than the Wiener filter can be constructed.

Variable span filters for speech enhancement

“…From (17) and (18), we see that there is a clear link between this and the maximum SNR filter. Hence, we propose a class of minimum distortion (MD) filters given by…”

“…This way, speech distortion can be traded for more noise reduction in a simple way by changing the number of eigenvectors. We also proposed enhancement filters based on the joint diagonalization in [17,18], but these were only derived for the single-channel case. Moreover, these enhancement methods used an indirect approach where the noise is estimated first and subtracted from the observation to obtain the enhanced signal, whereas the filters proposed herein estimates the desired signal directly.…”

A novel and integrated architecture for identification and cancellation of noise from GSM signal

“…This part of the study is a continuation of our prior review [11]. The work carried out by Norholm et al [12], have explored noise elimination issue in the time domain and used covariance matrices and optimal filtering approach for single-channel noise minimization. The performance analysis of the presented system is compared with the Wiener filter in terms of SNR.…”

Noise Reduction with Optimal Variable Span Linear Filters

“…This way, speech distortion can be traded for more noise reduction by changing the number of eigenvectors. We also proposed noise reduction filters based on the joint diagonalization in [25], [26]. As opposed to the filters proposed herein, these considered only an indirect approach where the noise is estimated first and subtracted from the observation to obtain the enhanced signal.…”