Overcoming the statistical independence assumption w.r.t. frequency in speech enhancement

In this paper, we give a solution on how to overcome the assumption of statistical independence of adjacent frequency bins in noise reduction techniques. We show that under relaxed assumptions the problem results in an a-priori SNR estimation problem, where all available noisy speech spectral amplitudes (observations) are exploited. Any state-of-the-art noise power spectral density (psd) estimation and weighting rule can be used - they do not need to be restated. In order to solve for an estimator well suited for real-time applications, we model the a-priori SNR values as Markov processes w.r.t. frequency. On the basis of the formulation by Ephraim and Malah, this leads to a new a-priori SNR estimator that yields fewer musical tones.