Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected remains an open area of research. This work, therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing, it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile ...

This thesis introduces TLM as a new method for modelling medical ultrasound wave propagation. Basic TLM theory is presented and how TLM is related to Huygens principle is discussed. Two dimensional TLM modelling is explained in detail and one dimensional and three dimensional TLM modelling are explained. Implementing TLM in single CPU computers and parallel computers is discussed and several algorithms are presented together with their advantages and disadvantages. Inverse TLM and modelling non linear wave propagation and different types of mesh are discussed. A new idea for modelling TLM as a digital filter is presented and removing the boundary effect based on digital filter modelling of TLM is discussed. Some modelling experiments such as : Focusing mirror. Circular mirror. Array transducers. Doppler effect. are presented and how to use TLM to model these experiments is explained. A new low ...

In order to find more sophisticated trends in data, potential correlations between larger and larger groups of variables must be considered. Unfortunately, the number of such correlations generally increases exponentially with the number of input variables and, as a result, brute force approaches become unfeasible. So, the data needs to be simplified sufficiently. Yet, the data may not be oversimplified. A method that is widely used for this purpose is to first cast the data as a matrix and the compute a low rank matrix approximation. The tight equivalences between the Weighted Low Rank Approximation (WLRA) problem and the Total Least Squares (TLS) problem are explored. Despite the seemingly different problem formulations of WLRA and TLS, it is shown that both methods can be reduced to the same mathematical kernel problem, i.e. finding the closest (in a certain sense) weighted ...

The widespread use of mobile internet and smart applications has led to an explosive growth in mobile data traffic. With the rise of smart homes, smart buildings, and smart cities, this demand is ever growing since future communication systems will require the integration of multiple networks serving diverse sectors, domains and applications, such as multimedia, virtual or augmented reality, machine-to-machine (M2M) communication / the Internet of things (IoT), automotive applications, and many more. Therefore, in the future, the communication systems will not only be required to provide Gbps wireless connectivity but also fulfill other requirements such as low latency and massive machine type connectivity while ensuring the quality of service. Without significant technological advances to increase the system capacity, the existing telecommunications infrastructure will be unable to support these multi-dimensional requirements. This poses an important demand for suitable waveforms with ...

This dissertation develops false discovery rate (FDR) controlling machine learning algorithms for large-scale high-dimensional data. Ensuring the reproducibility of discoveries based on high-dimensional data is pivotal in numerous applications. The developed algorithms perform fast variable selection tasks in large-scale high-dimensional settings where the number of variables may be much larger than the number of samples. This includes large-scale data with up to millions of variables such as genome-wide association studies (GWAS). Theoretical finite sample FDR-control guarantees based on martingale theory have been established proving the trustworthiness of the developed methods. The practical open-source R software packages TRexSelector and tlars, which implement the proposed algorithms, have been published on the Comprehensive R Archive Network (CRAN). Extensive numerical experiments and real-world problems in biomedical and financial engineering demonstrate the performance in challenging use-cases. The first three main parts of this dissertation present ...

MULTIPLE-INPUT MULTIPLE-OUTPUT (MIMO) CHANNELS constitute a unified way of modeling a wide range of different physical communication channels, which can then be handled with a compact and elegant vector-matrix notation. The two paradigmatic examples are wireless multi-antenna channels and wireline Digital Subscriber Line (DSL) channels. Research in antenna arrays (also known as smart antennas) dates back to the 1960s. However, the use of multiples antennas at both the transmitter and the receiver, which can be naturally modeled as a MIMO channel, has been recently shown to offer a significant potential increase in capacity. DSL has gained popularity as a broadband access technology capable of reliably delivering high data rates over telephone subscriber lines. A DSL system can be modeled as a communication through a MIMO channel by considering all the copper twisted pairs within a binder as a whole rather ...

Strong academic and commercial interest in image compression has resulted in a number of sophisticated compression techniques. Some of these techniques have evolved into international standards such as JPEG. However, the widespread success of JPEG has slowed the rate of innovation in such standards. Even most recent techniques, such as those proposed in the JPEG2000 standard, do not show significantly improved compression performance; rather they increase the bitstream functionality. Nevertheless, the manifold of multimedia applications demands for further improvements in compression quality. The problem of stagnating compression quality can be overcome by exploiting the limitations of the human visual system (HVS) for compression purposes. To do so, commonly used distortion metrics such as mean-square error (MSE) are replaced by an HVS-model-based quality metric. Thus, the "visual" quality is optimized. Due to the tremendous complexity of the physiological structures involved in ...

This thesis is concerned with three closely related problems. The first one is called Multiple-Input Multiple-Output (MIMO) Instantaneous Blind Identification, which we denote by MIBI. In this problem a number of mutually statistically independent source signals are mixed by a MIMO instantaneous mixing system and only the mixed signals are observed, i.e. both the mixing system and the original sources are unknown or ¡blind¢. The goal of MIBI is to identify the MIMO system from the observed mixtures of the source signals only. The second problem is called Instantaneous Blind Signal Separation (IBSS) and deals with recovering mutually statistically independent source signals from their observed instantaneous mixtures only. The observation model and assumptions on the signals and mixing system are the same as those of MIBI. However, the main purpose of IBSS is the estimation of the source signals, whereas ...

This thesis is concerned with three closely related problems. The first one is called Multiple-Input Multiple-Output (MIMO) Instantaneous Blind Identification, which we denote by MIBI. In this problem a number of mutually statistically independent source signals are mixed by a MIMO instantaneous mixing system and only the mixed signals are observed, i.e. both the mixing system and the original sources are unknown or ‘blind’. The goal of MIBI is to identify the MIMO system from the observed mixtures of the source signals only. The second problem is called Instantaneous Blind Signal Separation (IBSS) and deals with recovering mutually statistically independent source signals from their observed instantaneous mixtures only. The observation model and assumptions on the signals and mixing system are the same as those of MIBI. However, the main purpose of IBSS is the estimation of the source signals, whereas ...

Antenna arrays sample propagating waves at multiple locations. They are employed e.g. in radar, sonar and wireless communication systems because of their capacity of spatial selectivity and localization of radiating sources. Current model-based algorithms make use of computationally demanding orthogonal matrix decompositions such as the singular value decomposition (SVD). On the other hand the data rates are often extremely high. Therefore, real-time execution of complex algorithms often requires parallel computing. We study the simultaneous design of new algorithms and parallel architectures for subspace tracking, for robust adaptive beamforming and for direction finding of narrow-band and wide-band sources. By structuring all recursive algorithms in a similar way, they can be mapped efficiently onto the Jacobi architecture, which was originally developed for SVD updating. The numerical and architectural aspects of this algorithm are improved by the use of a minimal parameterziation of ...

A large variety of important tasks in low­-level vision, image analysis and pat­tern recognition can be formulated as discrete labeling problems where one seeks to optimize some measure of the quality of the labeling. For example such is the case in optical flow estimation, stereo matching, image restoration to men­tion only a few of them. Discrete Markov Random Fields are ideal candidates for modeling these labeling problems and, for this reason, they are ubiquitous in computer vision. Therefore, an issue of paramount importance, that has at­tracted a significant amount of computer vision research over the past years, is how to optimize discrete Markov Random Fields efficiently and accurately. The main theme of this thesis is concerned exactly with this issue. Two novel MRF op­timization schemes are thus presented, both of which manage to extend current state-­of­-the­-art techniques in significant ways. ...

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

This thesis treats efficient estimation algorithms for the epipolar geometry, the model underlying two views of the same scene or object. The epipolar geometry is computed from image correspondences that are found by local feature matching. These correspondences are used to calculate the fundamental matrix, which is the mathematical representation of the epipolar geometry. Since there are outliers among the correspondences, the fundamental matrix is usually calculated by the robust RANSAC (RANdom SAmple Consensus) algorithm which is very well suited for this purpose. A disadvantage of the algorithm, however, is that it shows a considerable complexity for higher outlier ratios. This hampers its application in vision algorithms dealing with many views. In this thesis we investigate techniques for faster fundamental matrix estimation using RANSAC. The first approach that is taken is the computation of inlier probabilities for the correspondences, that ...

In order to improve communication over a dispersive channel in a CDMA system, we have to re-establish the orthogonally of codes which are used when combining input signals from many users onto a single communication path, as otherwise the performance of such system is limited significantly by inter-symbol interference (ISI) and multiuser access interference (MAI). In order to achieve this, adaptive filters are employed. A variety of adaptive schemes to remove ISI and MAI have been reported in the literature, some of which rely on training sequences, such as the Least Mean Squares (LMS) and Recursive Least Squares (RLS) algorithms, or on blind adaptation, such as the Constant Modulus Algorithm (CMA) or the Decision Directed algorithm (DD), which has similar convergence properties as the LMS in the absence of decision errors, the CMA is relatively slow compared to the DD ...

Modern society is undergoing a fundamental change in the way we interact with technology. More and more devices are becoming "smart" by gaining advanced computation capabilities and communication interfaces, from household appliances over transportation systems to large-scale networks like the power grid. Recording, processing, and exchanging digital information is thus becoming increasingly important. As a growing share of devices is nowadays mobile and hence battery-powered, a particular interest in efficient digital signal processing techniques emerges. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. These may not always result in the best possible system performance. However, they often come close while being significantly simpler to describe and to implement. The simpler description facilitates a thorough analysis of their performance which is crucial to design robust and reliable ...