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