A new technique for blind reconstruction of stochastic processes with applications to speech enhancement

The need for reconstructing an unobserved and inaccessible stochastic process is widely encountered in diverse fields such as image restoration, speech signal restoration, data transmission, reflection seismology and functional magnetic resonance imaging. For instance, a typical communication system consists of a transmitter, a channel, and a receiver, where the channel represents all the interconnections between the transmitter and the receiver. A transmitted statistical signal is sent through an unknown channel whose output is the receiver input. The function of the receiver is to restore the original input from the observed signal. When the channel is imperfect and noisy, the restoration of the input signal becomes a very difficult task. This problem has been widely studied in the past and is still under investigation. This dissertation presents a new scheme for the reconstruction of an unobserved signal, which has been degraded by additive noise and convolutional noise. The proposed technique is a combination of cumulant-based blind deconvolution algorithms of different orders. It makes use of the order selection optimization and the de-noising ability of low-rank modeling theory. In addition, unlike most of the iterative blind deconvolution algorithms previously presented in the literature, the proposed algorithm possesses a convergence criterion. Due to its unique features, which are the use of a combination of several statistics of different order, its de-noising ability and its convergence criterion, the proposed algorithm is very attractive for a wide range of applications. Assuming knowledge of the variance of the unknown (unobserved) stochastic excitation process and under practical assumptions of stationarity and ergodicity, the technique satisfactorily restores the desired unobserved input in many situations. The performance of the proposed algorithm is evaluated using Monte Carlo simulation and short segments of recorded voiced speech utterances as realizations of random processes. These simulation studies show the algorithm to compare favorably with Shalvi and Weinstein\u27s algorithm, which is one of the most popular existing blind deconvolution algorithms. Sensitivity analysis using perturbation theory of the associated eigenvalue-eigenvector problem is included. The proposed algorithm with minor changes is combined with a proposed wavelet-based de-noising algorithm to implement a speech enhancement algorithm. This proposed technique improves speech quality by removing additive noise and, unlike most of the speech enhancement algorithms proposed in the literature, convolutional noise as well. (A typical example of convolutional noise is the distortion induced by a signal-distorting transmission channel.) In our context, the additive noise is assumed to be white and to have a Gaussian distribution. The proposed technique is very flexible in the sense that it can be combined with other existing noise reduction techniques in situations where the noise level is very high. Moreover, due to its distinguishing feature of dealing with convolutional noise, the proposed algorithm may be appropriate in applications where speech enhancement is needed in order to facilitate communication and intelligibility by machine recognizers