During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

The problem of signal separation is a very broad and fundamental one. A powerful paradigm within which signal separation can be achieved is the assumption that the signals/sources are statistically independent of one another. This is known as Independent Component Analysis (ICA). In this thesis, the theoretical aspects and derivation of ICA are examined, from which disparate approaches to signal separation are drawn together in a unifying framework. This is followed by a review of signal separation techniques based on ICA. Second order statistics based output decorrelation methods are employed to try to solve the challenging problem of separating convolutively mixed signals, in the context of mainly audio source separation and the Cocktail Party Problem. Various optimisation techniques are devised to implement second order signal separation of both artificially mixed signals and real mixtures. A study of the advantages and ...

The topic of this thesis is methods of pre-processing speech signals for robust estimation of model parameters in models of these signals. Here, there is a special focus on the situation where the desired signal is contaminated by colored noise. In order to estimate the speech signal, or its voiced and unvoiced components, from a noisy observation, it is important to have robust estimators that can handle colored and non-stationary noise. Two important aspects are investigated. The first one is a robust estimation of the speech signal parameters, such as the fundamental frequency, which is required in many contexts. For this purpose, fast estimation methods based on a simple white Gaussian noise (WGN) assumption are often used. To keep using those methods, the noisy signal can be pre-processed using a filter. If the colored noise is modelled as an autoregressive ...

This dissertation is concerned with the development of new optimal techniques for the solution of signal processing problems involving impulsive data. Although the signal processing and communications field has been dominated by the Gaussian distribution, it has been common knowledge that atmospheric noise, underwater acoustic noise, electro-magnetic disturbances on telephone lines and nancial time series showed an impulsive character which cannot be described by a Gaussian distribution. Recently, there has been great interest in the alpha-stable distribution. This thesis, in agreement with some of the recent work defends the alpha-stable model for impulsive data. Justications for the alpha-stable model are given and various analytical properties of these distributions are discussed. This discussion leads us to the minimum dispersion criterion which is the analogue of the minimum mean squared error criterion for alpha-stable distributed data. Based on the minimum dispersion criterion, ...

Reverberation is the sum of reflected sound waves and is present in any conventional room. Speech communication devices such as mobile phones in hands-free mode, tablets, smart TVs, teleconferencing systems, hearing aids, voice-controlled systems, etc. use one or more microphones to pick up the desired speech signals. When the microphones are not in the proximity of the desired source, strong reverberation and noise can degrade the signal quality at the microphones and can impair the intelligibility and the performance of automatic speech recognizers. Therefore, it is a highly demanded task to process the microphone signals such that reverberation and noise are reduced. The process of reducing or removing reverberation from recorded signals is called dereverberation. As dereverberation is usually a completely blind problem, where the only available information are the microphone signals, and as the acoustic scenario can be non-stationary, ...

High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identifi ed structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series influence each other. The goal of this dissertation pertains to study the problem of sparse topology identi fication under various settings. Topology identi fication from time series is a challenging task. The first major challenge in topology identi fication is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving ...

Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods. Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both ...

Reducing interference noise in a noisy speech recording has been a challenging task for many years yet has a variety of applications, for example, in handsfree mobile communications, in speech recognition, and in hearing aids. Traditional single-channel noise reduction schemes, such as Wiener filtering, do not work satisfactorily in the presence of non-stationary background noise. Alternatively, supervised approaches, where the noise type is known in advance, lead to higher-quality enhanced speech signals. This dissertation proposes supervised and unsupervised single-channel noise reduction algorithms. We consider two classes of methods for this purpose: approaches based on nonnegative matrix factorization (NMF) and methods based on hidden Markov models (HMM). The contributions of this dissertation can be divided into three main (overlapping) parts. First, we propose NMF-based enhancement approaches that use temporal dependencies of the speech signals. In a standard NMF, the important temporal ...

This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied. The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing. The nonlinear state estimation problem is ...

Never before has speech been captured as often by electronic devices equipped with one or multiple microphones, serving a variety of applications. It is the key aspect in digital telephony, hearing devices, and voice-driven human-to-machine interaction. When speech is recorded, the microphones also capture a variety of further, undesired sound components due to adverse acoustic conditions. Interfering speech, background noise and reverberation, i.e. the persistence of sound in a room after excitation caused by a multitude of reflections on the room enclosure, are detrimental to the quality and intelligibility of target speech as well as the performance of automatic speech recognition. Hence, speech enhancement aiming at estimating the early target-speech component, which contains the direct component and early reflections, is crucial to nearly all speech-related applications presently available. In this thesis, we compare, propose and evaluate existing and novel approaches ...

Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo ...

In this thesis a number of improvements have been established for specific methods which utilize sequential Monte Carlo (SMC), aka. Particle filtering (PF) techniques. The first problem is the Bayesian multi-target tracking (MTT) problem for which we propose the use of non-parametric Bayesian models that are based on time varying extension of Dirichlet process (DP) models. The second problem studied in this thesis is an important application area for the proposed DP based MTT method; the tracking of vocal tract resonance frequencies of the speech signals. Lastly, we investigate SMC based parameter estimation problem of nonlinear non-Gaussian state space models in which we provide a performance improvement for the path density based methods by utilizing regularization techniques.

The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

For humans, the sound is valuable mostly for its meaning. The voice is spoken language, music, artistic intent. Its physiological functioning is highly developed, as well as our understanding of the underlying process. It is a challenge to replicate this analysis using a computer: in many aspects, its capabilities do not match those of human beings when it comes to speech or instruments music recognition from the sound, to name a few. In this thesis, two problems are investigated: the source separation and the musical processing. The first part investigates the source separation using only one Microphone. The problem of sources separation arises when several audio sources are present at the same moment, mixed together and acquired by some sensors (one in our case). In this kind of situation it is natural for a human to separate and to recognize ...

Understanding speech in noise and the occurrence of acoustic feedback belong to the major problems of current hearing aid users. Hence, an urgent demand exists for efficient and well-working digital signal processing algorithms that offer a solution to these issues. In this thesis we develop adaptive filtering techniques for noise reduction and acoustic feedback cancellation. Thanks to the availability of low power digital signal processors, these algorithms can be integrated in a hearing aid. Because of the ongoing miniaturization in the hearing aid industry and the growing tendency towards multi-microphone hearing aids, robustness against imperfections such as microphone mismatch, has become a major issue in the design of a noise reduction algorithm. In this thesis we propose multimicrophone noise reduction techniques that are based on multi-channel Wiener filtering (MWF). Theoretical and experimental analysis demonstrate that these MWF-based techniques are less ...