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 ...

Digital visual communication has been increasingly adopted as an efficient new medium in a variety of different fields; multi-media computers, digital televisions, telecommunications, etc. Exchange of visual information between remote sites requires that digital video is encoded by compressing the amount of data and transmitting it through specified network connections. The compression and transmission of digital video is an amalgamation of statistical data coding processes, which aims at efficient exchange of visual information without technical barriers due to different standards, services, media, etc. It is associated with a series of different disciplines of digital signal processing, each of which can be applied independently. It includes a few different technical principles; distortion, rate theory, prediction techniques and control theory. The MPEG (Moving Picture Experts Group) video compression standard is based on this paradigm, thus, it contains a variety of different coding ...

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 ...

According to the Parkinson’s Foundation, more than 10 million people world- wide suffer from Parkinson’s disease (PD). The common symptoms are tremor, muscle rigidity and slowness of movement. There is no cure available cur- rently, but clinical intervention can help alleviate the symptoms significantly. Recently, it has been found that PD can be detected and telemonitored by voice signals, such as sustained phonation /a/. However, the voiced-based PD detector suffers from severe performance degradation in adverse envi- ronments, such as noise, reverberation and nonlinear distortion, which are common in uncontrolled settings. In this thesis, we focus on deriving speech modeling and robust estima- tion algorithms capable of improving the PD detection accuracy in adverse environments. Robust estimation algorithms using parametric modeling of voice signals are proposed. We present both segment-wise and sample-wise robust pitch tracking algorithms using the harmonic model. ...

In this thesis, advanced robust estimation methodologies for signal processing are developed and analyzed. The developed methodologies solve problems concerning multi-sensor data, robust model selection as well as robustness for dependent data. The work has been applied to solve practical signal processing problems in different areas of biomedical and array signal processing. In particular, for univariate independent data, a robust criterion is presented to select the model order with an application to corneal-height data modeling. The proposed criterion overcomes some limitations of existing robust criteria. For real-world data, it selects the radial model order of the Zernike polynomial of the corneal topography map in accordance with clinical expectations, even if the measurement conditions for the videokeratoscopy, which is the state-of-the-art method to collect corneal-height data, are poor. For multi-sensor data, robust model order selection selection criteria are proposed and applied ...

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, ...

Sigma delta modulation has become a widespread method of analogue to digital conversion, however its operation has not been completely defined. The majority of the analysis carried out on the circuit has been from a linear standpoint, with non-linear analysis hinting at hidden complexities in the modulator’s operation. The sigma delta modulator itself is a non-linear system consisting, as it does, of a number of integrators and a one bit quantiser in a feedback loop. This configuration can be generalised as a non-linearity within a feedback path, which is a classic route to chaotic behaviour. This initially raises the prospect that a sigma delta modulator may be capable of chaotic modes of operation with a non-chaotic input. In fact, the problem does not arise and we show why not. To facilitate this investigation, a set of differential equations is formulated ...

In numerous signal processing applications one disposes of multiple probes, delivering simultaneously information about one or multiple observed processes. The resulting multidimensional time series are often highly redundant and may contain stochastic contributions. The perception of the useful information becomes therefore very difficult and sometimes impossible. Thus, the major issue of concern of this thesis resides in the development of novel algorithms for the extraction of the salient and characteristic features of multidimensional time series. The proposed algorithms are based on parametric signal processing, namely we assume that the features of the experimental data can be represented efficiently by a specific model. We present a global framework for the selection of a specific model out of the large span of techniques proposed in the literature. For the selection of the model classes we use, in addition to prior knowledge about ...

Room acoustic signal enhancement (RASE) applications, such as digital equalization, acoustic echo and feedback cancellation, which are commonly found in communication devices and audio equipment, aim at processing the acoustic signals with the final goal of improving the perceived sound quality in rooms. In order to do so, signal processing algorithms require the acoustic response of the room to be represented by means of parametric models and to be identified from the input and output signals of the room acoustic system. In particular, a good model should be both accurate, thus capturing those features of room acoustics that are physically and perceptually most relevant, and efficient, so that it can be implemented as a digital filter and used in practical signal processing tasks. This thesis addresses the fundamental question in room acoustic signal processing concerning the appropriateness of different parametric ...

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 ...

With the advent of spectrally efficient wireless communication systems employing modulation schemes with varying amplitude of the communication signal, linearisation techniques for nonlinear microwave power amplifiers have gained significant interest. The availability of fast and cheap digital processing technology makes digital pre-distortion an attractive candidate as a means for power amplifier linearisation since it promises high power efficiency and fleexibility. Digital pre-distortion is further in line with the current efforts towards software defined radio systems, where a principal aim is to substitute costly and inflexible analogue circuitry with cheap and reprogrammable digital circuitry. Microwave power amplifiers are most efficient in terms of delivered microwave output power vs. supplied power if driven near the saturation point. In this operational mode, the amplifier behaves as a nonlinear device, which introduces undesired distortions in the information bear- ing microwave signal. These nonlinear distortions ...

Audio signals are characterised and perceived based on how their spectral make-up changes with time. Uncovering the behaviour of latent spectral components is at the heart of many real-world applications involving sound, but is a highly ill-posed task given the infinite number of ways any signal can be decomposed. This motivates the use of prior knowledge and a probabilistic modelling paradigm that can characterise uncertainty. This thesis studies the application of Gaussian processes to audio, which offer a principled non-parametric way to specify probability distributions over functions whilst also encoding prior knowledge. Along the way we consider what prior knowledge we have about sound, the way it behaves, and the way it is perceived, and write down these assumptions in the form of probabilistic models. We show how Bayesian time-frequency analysis can be reformulated as a spectral mixture Gaussian process, ...

Modern modulation methods as used in 3rd generation mobile communications (UMTS) generate strongly fluctuating transmission signal envelopes with high peak-to-average power ratios. These properties result in significant distortion due to the nonlinear behavior of the radio-frequency power amplifier (RF PA). We propose different nonlinear model structures for such amplifiers, based on memory polynomials and frequency-domain Volterra kernel expansion, where we can reduce the number of free parameters by 80% compared to traditional Volterra series approaches. Because these nonlinear models incorporate memory, we are able to model the nonlinear distortion of RF PAs with sufficient accuracy (e.g., −30 dB relative modeling error ), including the wideband case (bandwidth B = 20 MHz as needed for four-carrier WCDMA). Furthermore, we propose a method to construct RF PA models from frequency-dependent AM/AM and AM/PM conversions. For the compensation of the nonlinearities, we analyze ...

This thesis introduces the rank-order model and investigates its use in several image restoration problems. More commonly used as filters, the rank-order operators are here employed as predictors. A Laplacian excitation sequence is chosen to complete the model. Images are generated with the model and compared with those formed with an AR model. A multidimensional rankorder model is formed from vector medians for use with multidimensional image data. The first application using the rank-order model is an impulsive noise detector. This exploits the notion of ‘multimodality’ in the histogram of a difference image of the degraded image and a rank-order filtered version. It uses the EM algorithm and a mixture model to automatically determine thresholds for detecting the impulsive noise. This method compares well with other detection methods, which require manual setting of thresholds, and to stack filtering, which requires ...

Parametric modelling of speech signals finds its use in various speech processing applications. Recently, publications concerning sinusoidal speech modelling have been increasingly appeared in scientific literature. The thesis is mainly devoted to the sinusoidal model with harmonically related component sine waves, i.e. the harmonic model. The main objective is to find new approaches to synthetic speech quality improvement. A novel method for speech spectrum envelope determination is introduced. This method uses a staircase envelope considering the spectral behaviour in voiced as well as unvoiced speech frames. The staircase envelope is smoothed by weighted moving average. The determined envelope is parametrized using autoregressive (AR) model or cepstral coefficients. It has been shown that the new method is of most importance in high-pitch speakers. Besides, new methods or modifications of known methods can be found in pitch synchronization, AR model order selection ...