Some contributions to statistical signal processing and applications to audio enhancement and mobile localization

A random or stochastic process is a mathematical model for a phenomenon that evolves in time in an unpredictable manner from the viewpoint of the observer. It may be unpredictable due to the effect of the interference or noise in a communication link or storage medium, or it may be an information-bearing signal (deterministic from the viewpoint of the observer at the transmitter but random to an observer at the receiver). If prior information on the signal structure or statistics is available, the accuracy of the statistical signal processing significantly increases by an appropriate exploitation of such prior. In this thesis, we investigate three kinds of prior: spectral, spatial, and statistical information; and we consider applications to audio enhancement and mobile localization. First, we investigate the structural representation of audio signals. The proposed model exploits both the sparsity and the time-frequency correlation of the audio signal. We have considered the application of our model to audio enhancement and underdetermined audio separation. Experimental results reveal that the proposed approach is suitable for the analysis of music and speech signals, and produces good auditive synthetic results. Simulations show also that the proposed scheme outperforms the classic matching pursuit schemes in terms of separation accuracy and robustness. Then, we investigate blind dereverberation of audio signals. A multichannel linear prediction based equalizer is proposed, exploiting spatial, temporal, and spectral diversities. Simulations show that the proposed Delay-&-Predict equalizer outperforms the classic Delay-&-Sum beamformer. The last part of the thesis focuses on Bayesian parameter estimation. Classical Bayesian approaches lead to useful MSE reduction, but they also introduce a bias (often annoying for several applications). We introduce the concept of Component-Wise Conditionally Unbiased (CWCU) Bayesian parameter estimation, in which unbiasedness is forced for one parameter at a time. In such a way, every parameter in turn is treated as deterministic while the other parameters are treated as Bayesian. The more general introduction of the CWCU concept is motivated by LMMSE channel estimation, for which the implications of the concept are illustrated in various ways. Application to mobile localization is investigated in more details.