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 ...

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 ...

In this thesis, we consider the problem of decentralized estimation under communication constraints in the context of Collaborative Signal and Information Processing. Motivated by sensor network applications, a high volume of data collected at distinct locations and possibly in diverse modalities together with the spatially distributed nature and the resource limitations of the underlying system are of concern. Designing processing schemes which match the constraints imposed by the system while providing a reasonable accuracy has been a major challenge in which we are particularly interested in the tradeoff between the estimation performance and the utilization of communications subject to energy and bandwidth constraints. One remarkable approach for decentralized inference in sensor networks is to exploit graphical models together with message passing algorithms. In this framework, after the so-called information graph of the problem is constructed, it is mapped onto the ...

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

In this thesis, a general solution to the component separation problem in images is introduced. Unlike most existing works, the spatial dependencies of images are modelled in the separation process with the use of Markov random fields (MRFs). In the MRFs model, Cauchy density is used for the gradient images. We provide a general Bayesian framework for the estimation of the parameters of this model. Due to the intractability of the problem we resort to numerical solutions for the joint maximization of the a posteriori distribution of the sources, the mixing matrix and the noise variances. For numerical solution, four different methods are proposed. In first method, the difficulty of working analytically with general Gibbs distributions of MRF is overcome by using an approximate density. In this approach, the Gibbs distribution is modelled by the product of directional Gaussians. The ...

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 main objective of this thesis is to suggest a general Bayesian framework for model selection based on the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. In particular, we aim to reveal the undiscovered potentials of RJMCMC in model selection applications by exploiting the original formulation to explore spaces of di erent classes or structures and thus, to show that RJMCMC o ers a wider interpretation than just being a trans-dimensional model selection algorithm. The general practice is to use RJMCMC in a trans-dimensional framework e.g. in model estimation studies of linear time series, such as AR and ARMA and mixture processes, etc. In this thesis, we propose a new interpretation on RJMCMC which reveals the undiscovered potentials of the algorithm. This new interpretation, firstly, extends the classical trans-dimensional approach to a much wider meaning by exploring the spaces ...

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, ...

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 ...

The development of a fully unsupervised algorithm to achieve image segmentation is the central theme of this dissertation. Existing literature falls short of such a goal providing many algorithms capable of solving a subset of this highly challenging problem. Unsupervised segmentation is the process of identifying and locating the constituent regions of an observed image, while having no prior knowledge of the number of regions. The problem can be formulated in a Bayesian framework and through the use of an assumed model unsupervised segmentation can be posed as a problem of optimisation. This is the approach pursued throughout this dissertation. Throughout the literature, the commonly adopted model is an hierarchical image model whose underlying components are various forms of Markov Random Fields Gaussian. Markov Random Field models are used to model the textural content of the observed images regions, while ...

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 ...

In this dissertation we focus on statistical signal processing for Data Fusion, with a particular focus on wireless sensor networks. Six topics are studied: (i) Data Fusion for classification under model uncertainty; (ii) Decision Fusion over coherent MIMO channels; (iii) Performance analysis of Maximum Ratio Combining in MIMO decision fusion; (iv) Decision Fusion over non-coherent MIMO channels; (v) Decision Fusion for distributed classification of multiple targets; (vi) Data Fusion for inverse localization problems, with application to wideband passive sonar platform estimation. The first topic of this thesis addresses the problem of lack of knowledge of the prior distribution in classification problems that operate on small data sets that may make the application of Bayes' rule questionable. Uniform or arbitrary priors may provide classification answers that, even in simple examples, may end up contradicting our common sense about the problem. Entropic ...

In recent years, advances in signal processing have led the wireless sensor networks to be capable of mobility. The signal processing in a wireless sensor network differs from that of a traditional wireless network mainly in two important aspects. Unlike traditional wireless networks, in a sensor network the signal processing is performed in a fully distributed manner as the sensor measurements in a distributed fashion across the network collected. Additionally, due to the limited onboard resource of a sensor network it is essential to develop energy and bandwidth efficient signal processing algorithms. The thesis is devoted to discuss the state of the arte of algorithms commonly known as tracking algorithms. Although tracking algorithms have only been attracting research and development attention recently, already a wide literature and great variety of proposed approaches regarding the topic exist. The dissertation focus on ...

Mapping stationary objects and tracking moving targets are essential for many autonomous functions in vehicles. In order to compute the map and track estimates, sensor measurements from radar, laser and camera are used together with the standard proprioceptive sensors present in a car. By fusing information from different types of sensors, the accuracy and robustness of the estimates can be increased. Different types of maps are discussed and compared in the thesis. In particular, road maps make use of the fact that roads are highly structured, which allows relatively simple and powerful models to be employed. It is shown how the information of the lane markings, obtained by a front looking camera, can be fused with inertial measurement of the vehicle motion and radar measurements of vehicles ahead to compute a more accurate and robust road geometry estimate. Further, it ...

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 ...