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Speech signals radiated in confined spaces are subject to reverberation due to reflections of surrounding walls and obstacles. Reverberation leads to severe degradation of speech intelligibility and can be prohibitive for applications where speech is digitally recorded, such as audio conferencing or hearing aids. Dereverberation of speech is therefore an important field in speech enhancement. Driven by consumer demand, blind speech dereverberation has become a popular field in the research community and has led to many interesting approaches in the literature. However, most existing methods are dictated by their underlying models and hence suffer from assumptions that constrain the approaches to specific subproblems of blind speech dereverberation. For example, many approaches limit the dereverberation to voiced speech sounds, leading to poor results for unvoiced speech. Few approaches tackle single-sensor blind speech dereverberation, and only a very limited subset allows for dereverberation of speech from moving speakers. Therefore, the aim of this dissertation is the development of a flexible and extendible framework for blind speech dereverberation accommodating different speech sound types, single- or multiple sensor as well as stationary and moving speakers. Bayesian methods benefit from – rather than being dictated by – appropriate model choices. Therefore, the problem of blind speech dereverberation is considered from a Bayesian perspective in this thesis. A generic sequential Monte Carlo approach accommodating a multitude of models for the speech production mechanism and room transfer function is consequently derived. In this approach both the anechoic source signal and reverberant channel are estimated using their optimal estimators by means of Rao-Blackwellisation of the state-space of unknown variables. The remaining model parameters are estimated using sequential importance resampling. The proposed approach is implemented for two different speech production models for stationary speakers, demonstrating substantial reduction in reverberation for both unvoiced and voiced speech sounds. Furthermore, the channel model is extended to facilitate blind dereverberation of speech from moving speakers. Due to the structure of measurement model, single- as well as multi-microphone processing is facilitated, accommodating physically constrained scenarios where only a single sensor can be used as well as allowing for the exploitation of spatial diversity in scenarios where the physical size of microphone arrays is of no concern. This dissertation is concluded with a survey of possible directions for future research, including the use of switching Markov source models, joint target tracking and enhancement, as well as an extension to subband processing for improved computational efficiency.