Graph signal processing (GSP) extends classical signal processing to signals on graphs, enabling the analysis of complex data structures through graph theory. A core challenge in GSP is graph topology identification, which aims to deduce the graph structure that best explains observed signal dependencies.

This project addresses graph topology identification for applications where the underlying structure of systems like brain and social networks is not directly observable. Traditional approaches based on signal matching and spectral templates have limitations, particularly in handling scale issues and sparsity assumptions. We introduce a novel covariance matching methodology that efficiently reconstructs the graph topology using observable data. For the structural equation model (SEM) using an undirected graph, we demonstrate that our method can converge to the correct result under relatively soft conditions. Furthermore, we extend our methodology to polynomial models, sparse directed graphs, and any known Gaussian distribution of latent variables, broadening its applicability and utility in diverse graph-based systems. Experimental results demonstrate that our method outperforms existing techniques, offering new directions for future research in graph topology identification.

In this work, we deal with the problem of reconstructing a complete bandlimited graph signal from partially sampled noisy measurements. For a known graph structure, some efficient centralized algorithms are proposed to partition the nodes of the graph into disjoint subsets such that sampling the graph signal from any of these subsets leads to a sufficiently accurate reconstruction. Furthermore, we consider the situation when the graph has a massive size, where processing the data centrally is impractical anymore. To overcome this issue, a distributed framework is proposed that allows us to implement the centralized algorithms in a parallelized fashion. Finally, we provide numerical simulation results on synthetic and real-world data to show that our proposals outperform state-of-the-art node partitioning techniques.

The edge flow reconstruction task improves the integrity and accuracy of edge flow data by recovering corrupted or incomplete signals. This can be solved by a regularized optimization problem, and the corresponding regularizers are chosen based on prior knowledge. However, obtaining prior information is challenging in some fields. Thus, we consider exploiting the learning ability of neural networks to acquire prior knowledge. In this paper, we propose a new optimization problem for the simplicial edge flow reconstruction task, the simplicial ElasticNet, which is a regularized optimization problem that combines the advantages of the L1 and L2 norm. It is solved iteratively by the multi-block ADMM algorithm, and the convergence conditions are illustrated. By unrolling the simplicial ElasticNet's iterative steps, we propose a neural network with high interpretability and low requirement for the number of training data for the reconstruction task of simplicial edge flows. The unrolling network replaces the fixed parameters in the iterative algorithm with the learnable weights in the neural networks, thus exploiting the neural network's learning capability while preserving the iterative algorithm's interpretability. The core component of this unrolling network is simplicial convolutional filters with learnable weights to aggregate information from the edge flow neighbors, thus enhancing the learning and expressive ability of the network. We conduct extensive experiments on real-world and artificial datasets to validate the proposed approach. It is demonstrated that the simplicial unrolling network is significantly more advantageous than the traditional iterative algorithms and standard non-model-based neural networks in the case of limited training data.

Existing sonar systems typically rely on a minimum signal strength of a single echo, which limits their performance in low signal-to-noise conditions. This thesis explores the concept of coherent integration for active sonar, with the aim of improving imaging and detection capabilities under low signal-to-noise conditions. The goal is to provide signal processing methods that achieve long-time coherent integration of the received echoes, thereby maximising the processing gain. Additionally, this research explores waveform design by comparing the performance of pseudo-random noise with chirps. Two applications are seen in this thesis: moving target detection, which involves static sonar sensors, and synthetic aperture imaging, where the sensors move while the imaging scene remains static. For moving target detection, a processing methods is proposed which achieves coherent integration for constant velocity targets in a computationally efficient manner, and improves the detection performance by implementing a clutter filtering stage. For the second application, a processing method for imaging from a moving sensor pair is proposed. The resulting point-spread function for a circular sensor trajectory is investigated, from which a set of design rules are established. Additionally, a least squares algorithm is applied, which shows that the resulting image can be improved in terms of resolution and sidelobe interference. Finally, the imaging and detection methods are tested and verified using an in-air demonstrator.

In recent years, researchers proposed several universal caching policies. These universal caching policies aim to work well with any request sequence. However, with this universal well-working property, these caching policies sometimes do not work as well as conventional caching policies such as Least-Recently-Used and Least-Frequently-Used. This thesis introduces an online learning approach to dynamically switch between caching policies. The dynamical switching selects the most suitable caching policy for the request sequence and thus ensures the best of both worlds, working well under any request sequence and having comparable performance to the conventional caching policies. The Dynamic Expert Caching (DEC) policy designed in this thesis uses algorithms from the expert selection problem to achieve the dynamic caching policy selection. The DEC policy is evaluated using various datasets where it is shown to have comparable performance to the best caching policies in the simulations. The DEC policy is also adapted to work in a network of caches, named MultiDEC. In this setting, MultiDEC has significant advantages over other universal caching policies where each caching node can have a different caching policy that is optimal.

In the current Big Data era, large amounts of data are collected from complex systems, such as sensor networks and social networks. The emerging field of graph signal processing (GSP) leverages a network structure (graph) to process signals on an irregular domain. This thesis studies the forecasting of multi-dimensional graph processes, i.e., where each entity in the network carries a multivariate time series. Recent research has proposed to use product graphs to model the dependencies between different variables in multi-dimensional graph processes and employ them in graph-based vector autoregressive models to predict future values. A problem with these product graph-based models is that they can be too restrictive. In this work, it is proposed to combine product graph-based models with multiple one-dimensional models to implement more estimation flexibility. To further increase the degrees of freedom, the use of multiple-input-multiple-output graph filters is also proposed. The proposed models are implemented and tested on synthetic and real-world data sets, which shows an improved forecasting performance compared to state-of-the-art alternatives.

Networks with a large number of participants and a highly dynamic data exchange are better off using a distributed networking system due to network failures in centralized networks. However, with the increase in distributed networking, security problems arise in distributed processes. Injection of malicious data, for example, must be dealt with by using the tools provided by detection theory. The detection probability pd can be taken as the performance metric that we aim to optimize. In order to achieve this, one must first define a hypothesis testing problem and derive an optimization problem for pd that is dependent on which nodes are assumed to be compromised by these malicious agents that inject data.

For the injected data, there are three different models taken into consideration for the change in values over time and nodes. For every model, we assume that the outlier data can be injected with two different attack modes. These attack modes enforce different network topology related constraints on the set of compromised nodes due to different motivations. Furthermore, additional constraints are assumed due to the limited resources of the agents.
Additionally, with the given framework, we can also derive an optimization problem that can be solved with the help of the well-known linear regression method, i.e., Lasso. The problem that arise with this method is the difficulty of implementing the network topology related constraints into this optimization problem.

In order to solve these optimization problems, several methods are combined for the relaxation and solution of the optimization problems.

From numerical evaluation, it can be observed that our empirical performance is non-negligibly lower than the theoretical performance for all three models and both attacking modes. This can be linked to the dependence of the empirical distribution to the derived subset of compromised nodes, these subsets are chosen such that the cost function is optimized. Hence, we observe that the empirical values are much higher than it is theoretically assumed, in case that the network is 'clean'.
A second factor for performance evaluation is the number of wrongly indexed nodes, it can be observed how this factor is dependent on the distribution of the energy of the outlier data over the nodes and time.

Overall, this study shows that the provided framework shows an increasing performance for an increasing outlier-to-noise energy ratio. For an energy ratio higher than 0.5, the empirical and theoretical ROC-curves are nearly perfectly saturated for all models. The number of wrongly indexed nodes for our methods is generally speaking lower compared with the Lasso-method.

In the oil and gas industry a crucial step for detecting and developing natural resources is to drill wells and measure miscellaneous properties along the well depth. These measurements are used to understand the rock and hydrocarbon properties and support oil/gas field development. The measurements are done at multiple times and using different tools. This introduces multiple disturbances
which are not related to physical properties of rocks or fluids themselves, and should be tackled before data is used to build subsurface models or take decisions. One important source of this disturbances is depth misalignment and in order to compare different measurements care must be taken to ensure that all measurements (log curves) are properly positioned in depth. This process is called depth matching. In spite of multiple attempts for automating this process it is still mostly done manually. This thesis addresses the automation problem and proposing a model based approach to solve it using Parametric Time Warping (PTW).

Based on the PTW, a parameterised warping function that warps one of the curves is assumed and its parameters are determined by solving an optimization problem maximizing the cross-correlation between the two curves. The warping function is assumed to have the parametric form of a piecewise linear function in order to accommodate the linear shifts that take place during the measurement process. This method, combined with preprocessing techniques such as an offset correction and low pass filtering, gives a robust solution and can correctly align the most commonly accruing examples. Furthermore, the methodology is extended to depth match logs with severe distortion by applying the technique in an iterative fashion. Several examples are given when developed algorithm is tested on real log data supplemented with the analysis of the computational complexity this method has and the scalability to larger data sets.

On land, localization or ranging is typically performed by using electromagnetic waves. In an underwater environment, this becomes difficult, as electromagnetic waves dampen out fast. As a solution often acoustic waves are used to perform localization. Because of the complexity of underwater acoustic propagation, an acoustic propagation model is used of which the predicted output for different candidate locations is compared to the measurements. Methods to localize low-frequency sound sources with widely spaced receivers have been thoroughly studied in literature. More recently, also for high-frequency sources and receivers with a line-array structure successful localization has been demonstrated. In this thesis, the typical methods used to achieve this are gathered and typical challenges of these methods are identified. Based on these challenges, a new method is proposed, in an attempt to reduce the effects caused by these challenges and thus improve the localization performance. Also, Gibbs sampling is used to perform Bayesian inversion on the localization problem and simultaneously estimate environmental parameters. The results show that a high-frequency acoustic source at a range of 1500-2000m in an ocean environment with a depth of ∼ 200 meters can be localized by using the proposed method, including an accurately estimated tilt of the receiver array.

In this study multiple design approaches have been tried to accurately determine the respiratory rate every 30 seconds of a patient in a hospital bed using six piezoelectric pressure sensors located sand­wiched between the mattress and the bed. After four design iterations using a variety of different methods, a final design using a Least Mean Squares (LMS) filter and peak detection in the frequency domain was implemented. According to the test results, this method determines an accurate respira­tory rate 85% of the time in a controlled, experimental environment with the subject lying completely still. Unfortunately this accuracy is below the set requirements. However, it is believed that multiple improvements can still be made on the algorithm to increase the accuracy.

Detailed imaging of blood flow may improve the understanding of brain functions. The state-of-the-art non-invasive flow imaging of the brain is limited to a one-dimensional Doppler setting. We propose a method to estimate the two-dimensional flow vector in the fine vascular network of the brain by using a speckle tracking technique. The framework of Orthogonal Matching Pursuit is used for speckle tracking and modified to include prior constraints to guide the matching process among two frames, called as Guided Orthogonal Matching Pursuit. Prior constraint is in the form of a directional constraint which determines the probability of vector flow in all the directions according to the orientation of the vessels. The orientation of the vessels is computed using Power Doppler Imaging. In this work, the proposed method for two-dimensional vector estimation is compared with the standard block matching technique of Normalized Cross-Correlation. We see that the variance of the final velocity estimates has reduced when compared to the standard speckle tracking method and the direction of blood flow is found within the curvature of the vessel.

Electrical properties, the conductivity and permittivity of tissue, are quantities that describe the interaction of an object and electromagnetic fields. These properties influence electromagnetic fields and are influenced themselves by physiological phe- nomena such as lesions or a stroke. Therefore, they are important in identifying or diagnosing the severity of pathologies, and they are essential in magnetic resonance imaging (MRI) safety and efficiency by determining tissue heating or sensitivity to excitation pulses and antenna designs. In two-dimensional electromagnetic fields, which occur in specific measurement geometries, it is possible to simplify the relationship between electromagnetic fields and electrical properties, and reconstruct these properties using essentially a forward operation, foregoing a full inversion scheme. These insights also help to find, and ex- plain, the cause of specific artefacts, such as those caused by mismatches in incident field used in the computation of the full electromagnetic fields. The two-dimensional field assumption necessary for the simplified relationship described above is subsequently tested, and it is shown that this assumption does not hold when the object is sufficiently translation variant in the longitudinal direction. That is, even if the fields for a translation invariant object would be two-dimensional, they become three-dimensional through the interaction of the tissue parameters with the fields, which cause out of plane current and field contributions. Another interesting application of closed form expressions between currents and fields is the target field method, which solves the inverse source problem between electric currents and static magnetic fields in a regularised manner by constraining their relationship to a cylindrical geometry. This method is adapted for transverse oriented magnetic fields to be used with Halbach type magnet arrays, and an open source tool is developed to make the method easy to apply for various design con- siderations. Moving away from constraints on the field or current structure, we show the intri- cate relationship between electrical properties and the measured signal in an MRI scanner. This is done by deriving the electro- (and magneto-) motive force for a typ- ical MRI scenario without any assumptions on the object or electro-magnetic fields. This model can then even be used to reconstruct electrical properties from the sim- plest MRI signal, namely the free induced decay (FID) signal. To round off our investigation of tissue properties we take a small detour to the magnetic tissue property, the permeability or magnetic susceptibility. For reconstruct- ing this tissue property a dipole deconvolution is required, where the dipole convolu- tion loses information of the original object through the zeros of the dipole kernel. A new machine learning based approach to reconstruct the lost information is investi- gated in the final chapter of this thesis.@en

Previous work [1] has demonstrated the possibility of high resolution imaging through the use of a single element and a aberration mask. This thesis will expand on the previous work by examining the proposed method for errors in the creation of the model. The analysis is preformed by examining the various aspects of the measurements setup and underlying theoretical model, after which measurements are performed to determine their contribution and correctness with regard to the model. Results demonstrated a systematic error of a non-linear frequency scaling and semi-linear phase shift. The origin of the error lies in the unwanted addition of transfer functions of some of the components. A Tikhonov regularized least squares method is proposed to estimate this transfer function and supply compensation based on all the measurements. The results of application of this method on the uncalibrated model are demonstrated through 1D imaging experiments. The result of which show a signicant improvement over the previous uncalibrated results. After which the possibility of calibration due to a singular measurement is explored and a adaptation of the Tikhonov regularized least squares method is proposed for close approximation of the previously found transfer function. Further to obtain an indication of possible remaining hurdles and successes with this method, extensive simulations are preformed to examine the individual impact of various sources of noise and interference.

Ubiquitous connectivity requirements and stringent quality-of-services (QoS)
in recent wireless communications demand new revolutionary wireless network
technologies to support the exponentially increasing traffic growth.
Massive multiple-input-multiple-output (MIMO) with the capability of high
spectral efficiency achieved by large multiplexing and diversity gains grabbed
a lot of attention as a promising solution for future cellular networks. Achieving
ultra-reliable and low latency communication is very challenging without
increasing the network infrastructure cost, or extra processing complexity.
Adapting space-time-block-codes (STBC) can improve the reliability of
the system, but this increases the downlink pilot overhead. Two precoders
are devised to exploit full spatial diversity with the blind combining process
to avoid downlink pilot overhead.

In statistical learning over large data-sets, labeling all points is expensive and time-consuming. Semi-supervised classification allows learning with very few labels. Naturally, selecting a few points to label becomes crucial as the performance relies heavily on the labeled points. The motivation behind active learning is to build an optimal training set keeping the classifier in mind. Random or heuristic-driven selection does not care for the classification process or are trivially defined. We are interested in the graph structure formed by the data, as seen in citation, social and biological networks. Accordingly, active semi-supervised learning on graphs labels nodes to enhance the performance of classification. We propose a new methodology to perform active learning for diffusion-based semi-supervised classifiers. In particular, we focus on a classifier which diffuses probability distributions over the graph through random walks. We postulate the active learning problem as $i)$ a linear inverse problem with a sparse starting distribution over the nodes; $ii)$ a model output selection problem. For the former, we use sparsity-regularized inverse problems to select nodes. For the latter, we use tools from Compressed Sensing and Sparse Sensing to select the nodes with the relevant model output. We show that we can select all the relevant nodes in a single shot fashion, hence avoiding reliance on multiple training phases. Results on simulated as well as real data-sets show the proposed methods outperform random labeling, thereby proving to be relevant for active semi-supervised learning on graphs.

In this thesis, we investigate a sparse basis for ultrasound images, so that we can use sparse regularization in imaging. Actually, there are few previous researches explicitly demonstrating that medical ultrasound images can be sparsified for some dictionary. We consider various orthogonal transforms such as wavelet transforms, cosine transforms and wave atom transforms. Then, we perform those transforms on various ultrasound images and analyzes their sparsity. These ultrasound images include the images of two computer ultrasound phantoms and beamformed ultrasound images with good quality from real people. We looked at sparsity of the true pre-beamformed images, as well as beamformed images. We also consider constructing a specific ultrasound image dictionary using the K-SVD algorithm. We observed that, the pre-beamformed images hardly haVe no sparse basis, and the sparsity of beamformed images will only increase slightly if we use different 1D-DWT in each direction. We also found that the wide overdetermined dictionary generated by K-SVD significantly increases sparsity. After this, we simulate the ultrasound image reconstruction from the ultrasound RF measurements, and we analyze the effects of the different sparse spaces on the reconstruction performance. We observed that, the L1-regularization can work for ultrasound imaging better than L2-regularization, but the orthogonal transforms as well as the dictionary do not improve the reconstruction image quality much.

Nowadays, indoor ranging and localization have become necessary in daily life. Due to the multi-path propagation and noise in the indoor environment, phase domain ranging method using multi-frequency has been proposed which achieves accurate estimation of indoor target. However, as the indoor communication is usually carried on Bluetooth Low Energy (BLE) or Zigbee, high efficiency is indispensable in the face of limited bandwidth and measuring time. Thus, in this thesis, we aim to reduce the number of frequencies used in the ranging while keeping an acceptable estimation accuracy. We at first build the signal model and study the ambiguity range of the problem. Then based on the estimation theory and the concept of compressive sensing (CS) theory, we take the Cramer Rao Lower Bound (CRLB) and the matrix coherence as the criteria and select the optimal subset on given tone set. To test the performance of selected subset, we utilize gridless reconstruction algorithms, noiseless global matched filter (NL-GMF) and atomic norm minimization (ANM), to estimate target distance with the subset in both simulated data and real data and provide the mean square error (MSE), the estimation probability and the successful estimation probability in various estimation conditions.

The founders of Momo Medical envisioned a health care product that would help nurses worldwide with pressure ulcer prevention. Pressure ulcers are a chronic wound that affects the skin of patients who do not regularly change bed posture. As it currently stands, nurses lack the manpower and time to change the postureof patients in a timely manor. Thus, a goal was set to create a product that would reduce this strain on nurses.The goal was to design a non-intrusive product that keeps track of the posture of a patient on a hospital bed, and send an alarm if this has not changed in a set amount of time. A constraint with this was that the product has to lay directly underneath the mattress of the patient. Furthermore, the product has to make use of as few sensors as possible. With these constrains, the project group was divided in three subgroups: the sensor, the algorithm, and the testing subgroup.This report will focus on the design, implementation, and evaluation of the algorithm. The algorithm has to be designed to process the sensor data and return, with 90% accuracy, the posture of the patient. It also has to be able to determine with 99% accuracy whether or not there is a patient on the bed. An optional objective was to design an algorithm to determine the heart and respiration rate of the patient, with 80% accuracy, but this was of lower priority. It was soon decided to give priority to posture detection and not further investigate detection of the heart and respiration rate.In the final product, the information about the patient’s posture will be displayed in a graphical user interface (GUI). This GUI has to be user-friendly and intuitive to use by the nurses. During the prototyping phase, however, a different GUI was used, one that displayed various debugging information. This prototype GUI was necessary to test the various algorithms.Several different mathematical models have been investigated, implemented, and tested. These models range from taking the variance of the sensor data, to deploying a Fourier transform on a polynomial curve based on the sensor data. With preliminary test data, an accuracy of 93% was achieved using a neural network. With the final testing data however, only the neural network reached the required accuracy of 90%, though only just, at 90.8%. With future iterations of the algorithm, more research and data collection is advised, as neural networks work better with larger data sets.

In this thesis five different Direction Of Arrival algorithms will be developed for use with Microflown's Acoustic Vector Sensors, which will determine the direction an acoustic signal originates from. These algorithms will run on a main-station that will remotely receive data from an array of AVSs. The performance of these algorithms is examined using simulations and measurements obtained by a test setup. Finally, it is discussed under what circumstances which algorithm delivers the best performance.