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 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 ...

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 ...

Device-to-Device (D2D) is one of the important proposed solutions to increase the capacity, offload the traffic, and improve the energy effciency in next generation cellular networks. D2D communication is known as a direct communication between two users without using cellular infrastructure networks. Despite of large expected bene fits in terms of capacity in D2D, the coexistence of D2D and cellular networks in the same spectrum creates new challenges in interference management and network design. To limit the interference power control schemes on cellular networks and D2D networks are typically adopted. Even though power control is introduced to limit the interference level, it does not prevent cellular and D2D users from experiencing coverage limitation when sharing the same radio resources. Therefore, the design of such networks requires the availability of suitable methods able to properly model the eff ect of interference ...

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, ...

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 introduces new learning algorithms for Radial Basis Function (RBF) networks. RBF networks is a feed-forward two-layer neural network used for functional approximation or pattern classification applications. The proposed training algorithms are based on robust statistics. Their theoretical performance has been assessed and compared with that of classical algorithms for training RBF networks. The applications of RBF networks described in this thesis consist of simultaneously modeling moving object segmentation and optical flow estimation in image sequences and 3-D image modeling and segmentation. A Bayesian classifier model is used for the representation of the image sequence and 3-D images. This employs an energy based description of the probability functions involved. The energy functions are represented by RBF networks whose inputs are various features drawn from the images and whose outputs are objects. The hidden units embed kernel functions. Each kernel ...

In a natural acoustic environment, multiple sources are usually active at the same time. The task of source separation is the estimation of individual source signals from this complex mixture. The challenge of single channel source separation (SCSS) is to recover more than one source from a single observation. Basically, SCSS can be divided in methods that try to mimic the human auditory system and model-based methods, which find a probabilistic representation of the individual sources and employ this prior knowledge for inference. This thesis presents several strategies for the separation of two speech utterances mixed into a single channel and is structured in four parts: The first part reviews factorial models in model-based SCSS and introduces the soft-binary mask for signal reconstruction. This mask shows improved performance compared to the soft and the binary masks in automatic speech recognition ...

Multi-input multi-output (MIMO) wireless networks and distributed MIMO relaying wireless networks have attracted significant attention in current generation of wireless communication networks, and will play a key role in the next generation of wireless net- works. The improvement of network capacity, data rate and reliability can be achieved at the cost of increasing computational complexity of employing space-time coding (STC) and distributed STC (DSTC) in MIMO and distributed MIMO relaying networks, respectively. Efficient designs and algorithms to achieve high diversity and coding gains with low computational complexity in encoding and decoding of STC and DSTC schemes are essential. In this thesis, DSTC designs with high diversity and coding gains and efficient detection and code matrices optimization algorithms in cooperative MIMO networks are proposed. Firstly, adaptive power allocation (PA) algorithms with different criteria for a coop- erative MIMO network equipped with ...

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...

Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information, it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type of modeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and estimates the non-zero components. By modeling the detection problem as an array processing problem and a Bayesian filtering problem, we improve the detection accuracy. Bayesian methods approximate the sparsity by probability distributions which are iteratively modified. We show one approach to making the Bayesian method the Relevance Vector ...

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 ...

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 ...

Adaptive filtering techniques are used in a wide range of applications, including echo cancellation, adaptive equalization, adaptive noise cancellation, and adaptive beamforming. The performance of an adaptive filtering algorithm is evaluated based on its convergence rate, misadjustment, computational requirements, and numerical robustness. We attempt to improve the performance by developing new adaptation algorithms and by using "unconventional" structures for adaptive filters. Part I of this dissertation presents a new adaptation algorithm, which we have termed the Normalized LMS algorithm with Orthogonal Correction Factors (NLMS-OCF). The NLMS-OCF algorithm updates the adaptive filter coefficients (weights) on the basis of multiple input signal vectors, while NLMS updates the weights on the basis of a single input vector. The well-known Affine Projection Algorithm (APA) is a special case of our NLMS-OCF algorithm. We derive convergence and tracking properties of NLMS-OCF using a simple model ...

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 ...