Minimum Mean-Square Error Single-Channel Signal Estimation

This topic of this thesis is MMSE signal estimation for hearing aids when only one microphone is available. The research is relevant for noise reduction systems in hearing aids. To fully benefit from the amplification provided by a hearing aid, noise reduction functionality is important as hearing-impaired persons in some noisy situations need a higher signal to noise ratio for speech to be intelligible when compared to normal-hearing persons. In this thesis two different methods to approach the MMSE signal estimation problem is examined. The methods differ in the way that models for the signal and noise are expressed and in the way the estimator is approximated. The starting point of the first method is prior probability density functions for both signal and noise and it is assumed that their Laplace transforms (moment generating functions) are available. The corresponding posterior mean integral that defines the MMSE estimator is rewritten into an inverse Laplace transform integral over an integrand involving the moment generating functions. This integral is approximated using saddlepoint approximation. It is found that the saddlepoint approximation becomes inaccurate when two saddlepoints coalesce and a saddlepoint approximation based on two coalescing saddlepoints is derived. For practical reasons the method is limited to low dimensional problems and the results are not easily extended to the multivariate case. In the second approach signal and noise are specified by generative models and approximate inference is performed by particle filtering. The speech model is a time-varying auto-regressive model reparameterized by formant frequencies and bandwidths. The noise is assumed non-stationary and white. Compared to the case of using the AR coefficients directly then it is found very beneficial to perform particle filtering using the reparameterized speech model because it is relative straightforward to exploit prior information about formant features. A modified MMSE estimator is introduced and performance of the particle filtering algorithm is compared to a state of the art hearing aid noise reduction algorithm. Although performance of the two algorithms is found comparable then the particle filter algorithm is doing a much better job tracking the noise.