Joint estimation of signal and noise correlation matrices and its application to inverse filtering

Noise suppression by linear filters for a time series is discussed. We propose a method for jointly estimating signal and noise correlation matrices by incorporating steering vectors of the noise or eigenvectors of the noise correlation matrix as well as steering vectors of the target signals. Our estimates bring us two significant advantages. One is reduction of computational cost in obtaining the Wiener filter since the Wiener post filter, which is combined to the minimum variance distortionless response filter (MVDRF), is no longer needed with the estimates of signal and noise correlation matrices. The other is an improvement of the performance of the MVDRF since we can construct the regularized version of it with an estimate of the noise correlation matrix.

1. INTRODUCTION

Noise suppression for a time series is one of important topics in the field of speech and acoustic signal processing. As well known, one of popular methods for suppressing additive noise is the spectral subtraction (SS). Although this method effectively suppresses the noise, we have some difficulties to use it since it requires an estimate of the power of the noise and may generate a particular noise so-called ‘a musical noise’. A sensor-array-based noise suppression scheme is known as one of resolutions for these problems. The minimum variance distortionless response filter (MVDRF) and the Wiener filter (WF), which is implemented as the combination of the MVDRF and the Wiener post filter (WPF), are representative ones in the scheme. One of common and remarkable features of these methods is that they do not require the correlation structure of the noise.