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 ...

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

Typical acoustic scenes consist of multiple superimposed sources, where some of them represent desired signals, but often many of them are undesired sources, e.g., interferers or noise. Hence, source separation and extraction, i.e., the estimation of the desired source signals based on observed mixtures, is one of the central problems in audio signal processing. A promising class of approaches to address such problems is based on Independent Component Analysis (ICA), an unsupervised machine learning technique. These methods enjoyed a lot of attention from the research community due to the small number of assumptions that have to be made about the considered problem. Furthermore, the resulting generalization ability to unseen acoustic conditions, their mathematical rigor and the simplicity of resulting algorithms have been appreciated by many researchers working in audio signal processing. However, knowledge about the acoustic scenario is often available ...

This thesis addresses a number of issues concerned with the restoration of one type of image sequence namely archived black and white motion pictures. These are often a valuable historical record but because of the physical nature of the film they can suffer from a variety of degradations which reduce their usefulness. The main visual defects are ‘dirt and sparkle’ due to dust and dirt becoming attached to the film or abrasion removing the emulsion and ‘line scratches’ due to the film running against foreign bodies in the camera or projector. For an image restoration algorithm to be successful it must be based on a mathematical model of the image. A number of models have been proposed and here we explore the use of a general class of model known as Markov Random Fields (MRFs) based on Gibbs distributions by ...

Digital image acquisition is an intricate process, which is subject to various errors. Some of these errors are signal-dependent, whereas others are signal-independent. In particular, photon emission and sensing are inherently random physical processes, which in turn substantially contribute to the randomness in the output of the imaging sensor. This signal-dependent noise can be approximated through a Poisson distribution. On the other hand, there are various signal-independent noise sources involved in the image capturing chain, arising from the physical properties and imperfections of the imaging hardware. The noise attributed to these sources is typically modelled collectively as additive white Gaussian noise. Hence, we have three common ways of modelling the noise present in a digital image: Gaussian, Poisson, or Poisson-Gaussian. Image denoising aims at removing or attenuating this noise from the captured image, in order to provide an estimate of ...

This dissertation is concerned with the development of Markov chain Monte Carlo (MCMC) methods for the Bayesian restoration of degraded audio signals. First, the Bayesian approach to time series modelling is reviewed, then established MCMC methods are introduced. The first problem to be addressed is that of model order uncertainty. A reversible-jump sampler is proposed which can move between models of different order. It is shown that faster convergence can be achieved by exploiting the analytic structure of the time series model. This approach to model order uncertainty is applied to the problem of noise reduction using the simulation smoother. The effects of incorrect autoregressive (AR) model orders are demonstrated, and a mixed model order MCMC noise reduction scheme is developed. Nonlinear time series models are surveyed, and the advantages of linear-in- the-parameters models explained. A nonlinear AR (NAR) model, ...

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting a number of mutually independent elements from a set of observed linear mixtures. Motivated by various applications, this work considers a more general and more flexible model: the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups. We argue that this is tantamount to considering multidimensional components, as opposed to the standard ICA case which is restricted to one-dimensional components. In this work, we focus on second-order methods to separate statistically-independent multidimensional components from their linear instantaneous mixture. The purpose of this work is to provide theoretical answers to questions which so far have been discussed mainly in the empirical domain. Namely, we provide a closed-form expression for the figure of merit, the mean square error (MSE), for multidimensional ...

This dissertation deals with the design of satellite-based navigation receivers. The term Global Navigation Satellite Systems (GNSS) refers to those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the american GPS is probably the most popular, the european contribution (Galileo) will be operative soon. Other global and regional systems exist, all with the same objective: aid user's positioning. Initially, the thesis provides the state-of-the-art in GNSS: navigation signals structure and receiver architecture. The design of a GNSS receiver consists of a number of functional blocks. From the antenna to the fi nal position calculation, the design poses challenges in many research areas. Although the Radio Frequency chain of the receiver is commented in the thesis, the main objective of the dissertation is on the signal processing algorithms applied after signal digitation. These ...

Single channel source separation is a quite recent problem of constantly growing interest in the scientific world. However, this problem is still very far to be solved, and even more, it cannot be solved in all its generality. Indeed, since this problem is highly underdetermined, the main difficulty is that a very strong knowledge about the sources is required to be able to separate them. For a grand class of existing separation methods, this knowledge is expressed by statistical source models, notably Gaussian Mixture Models (GMM), which are learned from some training examples. The subject of this work is to study the separation methods based on statistical models in general, and then to apply them to the particular problem of separating singing voice from background music in mono recordings of songs. It can be very useful to propose some satisfactory ...

The separation of independent sources from mixed observed data is a fundamental and challenging signal processing problem. In many practical situations, one or more desired signals need to be recovered from the mixtures only. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. The audio signal separation problem is sometimes referred to as The Cocktail Party Problem. When several people in the same room are conversing at the same time, it is remarkable that a person is able to choose to concentrate on one of the speakers and listen to his or her speech flow unimpeded. This ability, usually referred to as the binaural cocktail party effect, results in part from binaural (two-eared) hearing. In contrast, ...

This dissertation investigates robust signal processing and machine learning techniques, with the objective of improving the robustness of two applications against various threats, namely Global Navigation Satellite System (GNSS) based positioning and satellite imaging. GNSS technology is widely used in different fields, such as autonomous navigation, asset tracking, or smartphone positioning, while the satellite imaging plays a central role in monitoring, detecting and estimating the intensity of key natural phenomena, such as flooding prediction and earthquake detection. Considering the use of both GNSS positioning and satellite imaging in critical and safety-of-life applications, it is necessary to protect those two technologies from either intentional or unintentional threats. In the real world, the common threats to GNSS technology include multipath propagation and intentional/unintentional interferences. This thesis investigates methods to mitigate the influence of such sources of error, with the final objective of ...

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 ...

Code-division multiple-access (CDMA) systems with random spreading and channel uncertainty at the receiver are studied. Frequency selective single antenna, as well as, narrowband multiple antenna channels are considered. Rayleigh fading is assumed in all cases. General Bayesian approach is used to derive both iterative and non-iterative estimators whose performance is obtained in the large system limit via the replica method from statistical physics. The effect of spatial correlation on the performance of a multiple antenna CDMA system operating in a flat-fading channel is studied. Per-antenna spreading (PAS) with random signature sequences and spatial multiplexing is used at the transmitter. Non-iterative multiuser detectors (MUDs) using imperfect channel state information (CSI) are derived. Training symbol based channel estimators having mismatched a priori knowledge about the antenna correlation are considered. Both the channel estimator and the MUD are shown to admit a simple ...

Radar backscatter from an ocean surface is commonly referred to as sea clutter. Any radar backscatter not due to the scattering from an ocean surface constitutes a potential target. This thesis is concerned with the study of target detection techniques in the presence of high resolution sea clutter. In this dissertation, the high resolution sea clutter is treated as a compound process, where a fast oscillating speckle component is modulated in power by a slowly varying modulating component. While the short term temporal correlations of the clutter are associated with the speckle, the spatial correlations are largely associated with the modulating component. Due to the disparate statistical and correlation properties of the two components, a piecemeal approach is adopted throughout this thesis, whereby the spatial and the temporal correlations of high resolution sea clutter are treated independently. As an extension ...

This thesis presents a comprehensive example framework on how current multiple model state estimation algorithms for jump Markov linear systems can be improved. The possible improvements are categorized as: -Design of multiple model state estimation algorithms using new criteria. -Improvements obtained using existing multiple model state estimation algorithms. In the first category, risk-sensitive estimation is proposed for jump Markov linear systems. Two types of cost functions namely, the instantaneous and cumulative cost functions related with risk-sensitive estimation are examined and for each one, the corresponding multiple model estate estimation algorithm is derived. For the cumulative cost function, the derivation involves the reference probability method where one defines and uses a new probability measure under which the involved processes has independence properties. The performance of the proposed risk-sensitive filters are illustrated and compared with conventional algorithms using simulations. The thesis addresses ...