Study of the frequency-domain multichannel noise reduction problem with the householder transformation

This paper presents an approach to the multichannel noise reduction problem. It first transforms the multichannel noisy speech signals into the frequency domain. A Householder transformation is then constructed, which converts the multichannel coefficients in each frequency bin into two components: one dominated by speech and the other dominated by noise. A Wiener filter is subsequently formed to achieve an estimate of the noise in the speech dominated component from the noise dominated component. The enhanced speech is then obtained by subtracting the noise estimate from the speech dominated component. This approach consists of two critical steps: construction of the Householder transformation and formation of the noise reduction Wiener filter. If the source incidence angle is known a priori, the Householder transformation can be directly constructed using the steering vector and the optimal estimate of the signal of interest can then be obtained by applying the Wiener filter. If the source incidence angle is not known a priori, the Householder transformation can be constructed from a hypothesized incidence angle. Then, the optimal signal estimate is obtained by searching the maximum of the variance of the enhanced signal with the Wiener filter in the interested range of the incidence angle.