Bayesian Compressed Sensing using Alpha-Stable Distributions

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 ...

Tzagkarakis, George — University of Crete

Adaptive Equalisation for Impulsive Noise Environments

This thesis addresses the problem of adaptive channel equalisation in environments where the interfering noise exhibits nonâ€“Gaussian behaviour due to impulsive phenomena. The family of alphaâ€“stable distributions has proved to be a suitable and flexible tool for the modelling of signals with impulsive nature. However, nonâ€“Gaussian alphaâ€“stable signals have infinite variance, and signal processing techniques based on second order moments are meaningless in such environments. In order to exploit the flexibility of the stable family and still take advantage of the existing signal processing tools, a novel framework for the integration of the stable model in a communications context is proposed, based on a finite dynamic range receiver. The performance of traditional signal processing algorithms designed under the Gaussian assumption may degrade seriously in impulsive environments. When this degradation cannot be tolerated, the traditional signal processing methods must be revisited ...

Georgiades, Apostolos Theofani — University Of Edinburgh

Sequential Bayesian Modeling of non-stationary signals

are involved until the development of Sequential Monte Carlo techniques which are also known as the particle filters. In particle filtering, the problem is expressed in terms of state-space equations where the linearity and Gaussianity requirements of the Kalman filtering are generalized. Therefore, we need information about the functional form of the state variations. In this thesis, we bring a general solution for the cases where these variations are unknown and the process distributions cannot be expressed by any closed form probability density function. Here, we propose a novel modeling scheme which is as unified as possible to cover all these problems. Therefore we study the performance analysis of our unifying particle filtering methodology on non-stationary Alpha Stable process modeling. It is well known that the probability density functions of these processes cannot be expressed in closed form, except for ...

Gencaga, Deniz — Bogazici University

Robust Methods for Sensing and Reconstructing Sparse Signals

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

Carrillo, Rafael — University of Delaware

Simulation Methods for Linear and Nonlinear Time Series Models with Application to Distorted Audio Signals

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, ...

Troughton, Paul Thomas — University of Cambridge

Speech Modeling and Robust Estimation for Diagnosis of Parkinson's Disease

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. ...

Shi, Liming — Aalborg University

Generalised Bayesian Model Selection Using Reversible Jump Markov Chain Monte Carlo

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 ...

Karakus, Oktay — Izmir Institute of Technology

Robust Estimation and Model Order Selection for Signal Processing

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 ...

Muma, Michael — Technische Universität Darmstadt

Adaptive filtering algorithms for acoustic echo cancellation and acoustic feedback control in speech communication applications

Multimedia consumer electronics are nowadays everywhere from teleconferencing, hands-free communications, in-car communications to smart TV applications and more. We are living in a world of telecommunication where ideal scenarios for implementing these applications are hard to find. Instead, practical implementations typically bring many problems associated to each real-life scenario. This thesis mainly focuses on two of these problems, namely, acoustic echo and acoustic feedback. On the one hand, acoustic echo cancellation (AEC) is widely used in mobile and hands-free telephony where the existence of echoes degrades the intelligibility and listening comfort. On the other hand, acoustic feedback limits the maximum amplification that can be applied in, e.g., in-car communications or in conferencing systems, before howling due to instability, appears. Even though AEC and acoustic feedback cancellation (AFC) are functional in many applications, there are still open issues. This means that ...

Gil-Cacho, Jose Manuel — KU Leuven

Maximum a posteriori Deconvolution of Ultrasonic Data with Applications in Nondestructive Testing: Multiple transducer and robustness issues

In the thesis, various aspects of deconvolution of ultrasonic pulse-echo signals in nondestructive testing are treated. The deconvolution problem is formulated as estimation of a reflection sequence which is the impulse characteristic of the inspected object and the estimation is performed using either maximum a posteriori (MAP) or linear minimum mean square error (MMSE) estimators. A multivariable model is proposed for a certain multiple transducer setup allowing for frequency diversity, thereby improving the estimation accuracy. Using the MAP estimator three different material types were treated, with varying amount of sparsity in the reflection sequences. The Gaussian distribution is used for modelling materials containing a large number of small scatters. The Bernoulli--Gaussian distribution is used for sparse data obtained from layered structures and a genetic algorithm approach is proposed for optimizing the corresponding MAP criterion. Sequences with intermediate sparsity suitable of ...

Olofsson, Tomas — Uppsala University

Bayesian Approaches in Image Source Seperation

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 ...

Kayabol, Koray — Istanbul University

Efficient parametric modeling, identification and equalization of room acoustics

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 ...

Vairetti, Giacomo — KU Leuven

Robust Algorithms for Linear and Nonlinear Regression via Sparse Modeling Methods: Theory, Algorithms and Applications to Image Denoising

The task of robust regression is of particular importance in signal processing, statistics and machine learning. Ordinary estimators, such as the Least Squares (LS) one, fail to achieve sufficiently good performance in the presence of outliers. Although the problem has been addressed many decades ago and several methods have been established, it has recently attracted more attention in the context of sparse modeling and sparse optimization techniques. The latter is the line that has been followed in the current dissertation. The reported research, led to the development of a novel approach in the context of greedy algorithms. The model adopts the decomposition of the noise into two parts: a) the inlier noise and b) the outliers, which are explicitly modeled by employing sparse modeling arguments. Based on this rationale and inspired by the popular Orthogonal Matching Pursuit (OMP), two novel ...

Papageorgiou, George — National and Kapodistrian University of Athens

Speech Enhancement Using Data-Driven Concepts

Speech communication frequently suffers from transmitted background noises. Numerous speech enhancement algorithms have thus been proposed to obtain a speech signal with a reduced amount of background noise and better speech quality. In most cases they are analytically derived as spectral weighting rules for given error criteria along with statistical models of the speech and noise spectra. However, as these spectral distributions are indeed not easy to be measured and modeled, such algorithms achieve in practice only a suboptimal performance. In the development of state-of-the-art algorithms, speech and noise training data is commonly exploited for the statistical modeling of the respective spectral distributions. In this thesis, the training data is directly applied to train data-driven speech enhancement algorithms, avoiding any modeling of the spectral distributions. Two applications are proposed: (1) A set of spectral weighting rules is trained from noise ...

The main objective of $\gamma$ spectrometry is to characterize the radioactive elements of an unknown source by studying the energy of the emitted $\gamma$ photons. When a photon interacts with a detector, its photonic energy is converted into an electrical pulse, whose integral energy is measured. The histogram obtained by collecting the energies can be used to identify radionucleides and measure their activity. However, at high counting rates, perturbations which are due to the stochastic aspect of the temporal signal can cripple the identification of the radioactive elements. More specifically, since the detector has a finite resolution, close arrival times of photons which can be modeled as an homogeneous Poisson process cause pileups of individual pulses. This phenomenon distorts energy spectra by introducing multiple fake spikes and prolonging artificially the Compton continuum, which can mask spikes of low intensity. The ...