## Sensing physical fields: Inverse problems for the diffusion equation and beyond (2016)

Cosparse regularization of physics-driven inverse problems

Inverse problems related to physical processes are of great importance in practically every field related to signal processing, such as tomography, acoustics, wireless communications, medical and radar imaging, to name only a few. At the same time, many of these problems are quite challenging due to their ill-posed nature. On the other hand, signals originating from physical phenomena are often governed by laws expressible through linear Partial Differential Equations (PDE), or equivalently, integral equations and the associated Green’s functions. In addition, these phenomena are usually induced by sparse singularities, appearing as sources or sinks of a vector field. In this thesis we primarily investigate the coupling of such physical laws with a prior assumption on the sparse origin of a physical process. This gives rise to a “dual” regularization concept, formulated either as sparse analysis (cosparse), yielded by a PDE ...

Kitić, Srđan — Université de Rennes 1

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

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 ...

van de Laar, Jakob — TU Eindhoven

MIMO instantaneous blind idenfitication and separation based on arbitrary order

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 ...

van de Laar, Jakob — T.U. Eindhoven

Sparse Sensing for Statistical Inference: Theory, Algorithms, and Applications

In today's society, we are flooded with massive volumes of data in the order of a billion gigabytes on a daily basis from pervasive sensors. It is becoming increasingly challenging to locally store and transport the acquired data to a central location for signal/data processing (i.e., for inference). To alleviate these problems, it is evident that there is an urgent need to significantly reduce the sensing cost (i.e., the number of expensive sensors) as well as the related memory and bandwidth requirements by developing unconventional sensing mechanisms to extract as much information as possible yet collecting fewer data. The first aim of this thesis is to develop theory and algorithms for data reduction. We develop a data reduction tool called sparse sensing, which consists of a deterministic and structured sensing function (guided by a sparse vector) that is optimally designed ...

Chepuri, Sundeep Prabhakar — Delft University of Technology

Deep neural networks for source separation and noise-robust speech recognition

This thesis addresses the problem of multichannel audio source separation by exploiting deep neural networks (DNNs). We build upon the classical expectation-maximization (EM) based source separation framework employing a multichannel Gaussian model, in which the sources are characterized by their power spectral densities and their source spatial covariance matrices. We explore and optimize the use of DNNs for estimating these spectral and spatial parameters. Employing the estimated source parameters, we then derive a time-varying multichannel Wiener filter for the separation of each source. We extensively study the impact of various design choices for the spectral and spatial DNNs. We consider different cost functions, time-frequency representations, architectures, and training data sizes. Those cost functions notably include a newly proposed task-oriented signal-to-distortion ratio cost function for spectral DNNs. Furthermore, we present a weighted spatial parameter estimation formula, which generalizes the corresponding exact ...

Nugraha, Aditya Arie — Université de Lorraine

Statistical Signal Processing for Data Fusion

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 ...

Ciuonzo, Domenico — Second University of Naples

Fading in Wearable Communications Channels and its Mitigation

The fabrication of miniature electronics and sensors has encouraged the creation of a wide range of wireless enabled devices designed to be worn on the human body. This has led to the prominence of so-called wearable communications, which have emerged to satisfy the demand for wireless connectivity between these devices and with external networks. The work in this thesis has focused on the characterization of the composite fading (i.e combined multipath and shadowing) observed in wearable communications channels. It has also investigated the mitigation of the deleterious effects of both of these propagation phenomena in wearable communications. In order to accurately characterize the behaviour of the composite fading signal observed in wearable communications channels, new fading models such as F, $\kappa$-$\mu$ / inverse gamma and $\eta$-$\mu$ / inverse gamma composite fading models, have been proposed. The generality and utility of ...

Seong Ki Yoo — Queen's University Belfast

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 ...

Antonello, Niccolò — KU Leuven

This dissertation deals with the distributed processing techniques for parameter estimation and efficient data-gathering in wireless communication and sensor networks. The estimation problem consists in inferring a set of parameters from temporal and spatial noisy observations collected by different nodes that monitor an area or field. The objective is to derive an estimate that is as accurate as the one that would be obtained if each node had access to the information across the entire network. With the aim of enabling an energy aware and low-complexity distributed implementation of the estimation task, several useful optimization techniques that generally yield linear estimators were derived in the literature. Up to now, most of the works considered that the nodes are interested in estimating the same vector of global parameters. This scenario can be viewed as a special case of a more general ...

Bogdanovic, Nikola — University of Patras

Signal processing algorithms for wireless acoustic sensor networks

Recent academic developments have initiated a paradigm shift in the way spatial sensor data can be acquired. Traditional localized and regularly arranged sensor arrays are replaced by sensor nodes that are randomly distributed over the entire spatial field, and which communicate with each other or with a master node through wireless communication links. Together, these nodes form a so-called ‘wireless sensor network’ (WSN). Each node of a WSN has a local sensor array and a signal processing unit to perform computations on the acquired data. The advantage of WSNs compared to traditional (wired) sensor arrays, is that many more sensors can be used that physically cover the full spatial field, which typically yields more variety (and thus more information) in the signals. It is likely that future data acquisition, control and physical monitoring, will heavily rely on this type of ...

Bertrand, Alexander — Katholieke Universiteit Leuven

The present doctoral thesis aims towards the development of new long-term, multi-channel, audio-visual processing techniques for the analysis of bioacoustics phenomena. The effort is focused on the study of the physiology of the gastrointestinal system, aiming at the support of medical research for the discovery of gastrointestinal motility patterns and the diagnosis of functional disorders. The term "processing" in this case is quite broad, incorporating the procedures of signal processing, content description, manipulation and analysis, that are applied to all the recorded bioacoustics signals, the auxiliary audio-visual surveillance information (for the monitoring of experiments and the subjects' status), and the extracted audio-video sequences describing the abdominal sound-field alterations. The thesis outline is as follows. The main objective of the thesis, which is the technological support of medical research, is presented in the first chapter. A quick problem definition is initially ...

Dimoulas, Charalampos — Department of Electrical and Computer Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

This thesis deals with the efficient and flexible acquisition and processing of spatial sound using multiple microphones. In spatial sound acquisition and processing, we use multiple microphones to capture the sound of multiple sources being simultaneously active at a rever- berant recording side and process the sound depending on the application at the application side. Typical applications include source extraction, immersive spatial sound reproduction, or speech enhancement. A flexible sound acquisition and processing means that we can capture the sound with almost arbitrary microphone configurations without constraining the application at the ap- plication side. This means that we can realize and adjust the different applications indepen- dently of the microphone configuration used at the recording side. For example in spatial sound reproduction, where we aim at reproducing the sound such that the listener perceives the same impression as if he ...

Thiergart, Oliver — Friedrich-Alexander-Universitat Erlangen-Nurnberg

Distributed Signal Processing Algorithms for Multi-Task Wireless Acoustic Sensor Networks

Recent technological advances in analogue and digital electronics as well as in hardware miniaturization have taken wireless sensing devices to another level by introducing low-power communication protocols, improved digital signal processing capabilities and compact sensors. When these devices perform a certain pre-defined signal processing task such as the estimation or detection of phenomena of interest, a cooperative scheme through wireless connections can significantly enhance the overall performance, especially in adverse conditions. The resulting network consisting of such connected devices (or nodes) is referred to as a wireless sensor network (WSN). In acoustical applications (e.g., speech enhancement) a variant of WSNs, called wireless acoustic sensor networks (WASNs) can be employed in which the sensing unit at each node consists of a single microphone or a microphone array. The nodes of such a WASN can then cooperate to perform a multi-channel acoustic ...

Hassani, Amin — KU Leuven

Variational Sparse Bayesian Learning: Centralized and Distributed Processing

In this thesis we investigate centralized and distributed variants of sparse Bayesian learning (SBL), an effective probabilistic regression method used in machine learning. Since inference in an SBL model is not tractable in closed form, approximations are needed. We focus on the variational Bayesian approximation, as opposed to others used in the literature, for three reasons: First, it is a flexible general framework for approximate Bayesian inference that estimates probability densities including point estimates as a special case. Second, it has guaranteed convergence properties. And third, it is a deterministic approximation concept that is even applicable for high dimensional problems where non-deterministic sampling methods may be prohibitive. We resolve some inconsistencies in the literature involved in other SBL approximation techniques with regard to a proper Bayesian treatment and the incorporation of a very desired property, namely scale invariance. More specifically, ...

Buchgraber, Thomas — Graz University of Technology

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