Complex systems and networks, including financial, brain, transport, and social networks, can be modeled as graphs. Learning their connectivity is valuable because structure drives dynamics, enabling prediction, monitoring, and control. Applications include understanding diseases such as Alzheimer’s, epilepsy, and other neurological disorders. Past work has emphasized static graphs with fixed connectivity, while more recent efforts address dynamic graphs that better reflect real-world networks. To accommodate time variation, online and recursive methods update connectivity estimates as new node signals arrive.

An online algorithm for graph topology identification, \textit{Kalman Dynamic Online GTI} (KalDO GTI), has been developed where the adjacency is the hidden state of a state–space model and is updated via a recursive Kalman filter. Beyond state tracking, the state transition matrix is also estimated online through an optimization loop and is refined with Adam-based updates under sparsity, masking, and structural priors. This two-tier structure, sequential Kalman prediction–correction for adjacency tracking and batch optimization for state dynamics learning, yields a recursive yet adaptive framework suited for online, streaming data. In direct comparison with streaming LASSO and prediction–correction methods, the algorithm is competitive across regimes and particularly robust under high measurement noise. Experiments on synthetic networks with aggressive dynamic regimes validate the approach and show similar or better performance compared to existing methods.

This thesis details the implementation and evaluation of seven machine learning classifiers for the detection of Autism Spectrum Disorder (ASD) using resting-state functional MRI (rs-fMRI) data from the ABIDE I dataset. Two feature representations were compared: traditional Pearson correlation features and graph-based features. Logistic Regression (LR), Support Vector Machine (SVM), and Multi-Layer Perceptron (MLP) achieved the highest performance on Pearson correlation features, satisfying all predefined non-functional requirements, with average balanced accuracies up to 64.4% (SVM) and standard deviations below 2.5%. Linear Discriminant Analysis (LDA) narrowly missed the standard deviation constraint with 0.5%.
In contrast to the Pearson correlation features, graph-based features yielded consistently lower balanced accuracies, typically ranging from 54% to 59% across classifiers, underscoring their limited informativeness in the current implementation. Feature importance analysis on Pearson correlation data revealed connections between brain regions involving the inferior occipital gyrus, middle temporal pole, precuneus, and cerebellum as
consistently influential for classification. To facilitate neuroscientific exploration, an interactive tool, NASDA (Neuroimaging Autism Spectrum Disorder Analyser), was developed and demonstrated to fulfil all functional and non-functional requirements for Pearson correlation based analysis using LR as the recommended classification model.
These results highlight the dependency of classifiers performance on the quality of input features and contribute to ongoing efforts to localise robust neurological biomarkers for ASD.

Synthetic Aperture Sonar (SAS) is an advanced sonar imaging technique that uses multiple pulses or high duty cycle waveforms from a moving surface vehicle to create a synthetic aperture array for imaging. One of the key challenges of SAS systems is the design of continuous waveforms that enable high-quality imaging under practical constraints (e.g., unimodular constraint). This thesis addresses the design of such waveforms and observes that waveform design for a SAS system over a short time window can be approximated as a wideband ambiguity function shaping problem. To tackle this, we formulate the wideband ambiguity function shaping problem as a non-convex optimization problem and propose four methods to solve it. Among the proposed methods, the wideband gradient descent method is proven to be the most efficient and effective in minimizing the average sidelobe energy in the region of interest of the wideband ambiguity function. Simulation and field trial results show that, although waveform design for SAS systems is not strictly equivalent to wideband ambiguity function shaping, the waveform obtained through this approach still yields good SAS imaging performance compared to conventional sonar waveforms, such as the random Binary Phase-Shift Keying (BPSK) waveform. These findings provide a direction for the waveform design of future SAS systems. Beyond SAS, the proposed wideband ambiguity function shaping methods also show potential for other wideband applications, such as waveform design for underwater target tracking.

In the Netherlands, 3% of people above 4 years old are diagnosed with autism. Diagnosing is currently done with a psychological assessment, but classifying people with autism using resting state functional magnetic imaging, or rs-fMRI, has become promising. The goal of this project was to see if new features could be found, based on the graph of rs-fMRI data stored in the Autism Brain Imaging Data Exchange (ABIDE) dataset, that had a significant positive influence on the accuracy of a predictive model. To do this, several feature selection modules were researched and coded in Python. Subsequently, these were tested with the features and classification methods created by our partner subgroups. The best performing model, using all data, had an accuracy of 74.26% and a sensitivity of 65.35%. The best performing model using graph features, on all data, had an accuracy of 60.4% and a sensitivity of 46.6%. This indicates that there were no graph features developed that had a significant positive influence on classifying whether someone has autism.

This research is part of a broader study on Autism Spectrum Disorder (ASD) detection, which consists of three main components: feature design, classification, and feature selection. The primary objective of this study is to investigate whether different graph inference methods and graph-based features can contribute to finding new biomarkers in the brains of individuals with ASD. To easily interpret and visualize the results, a graphical user interface (GUI) was developed. The feature design phase includes both classical statistical features and innovative graph-based features, derived through a variety of statistical and Graph Signal Processing (GSP) graph inference methods. The top three performing methods were: sample covariance with graphical lasso (59.3% accuracy, 64.2% AUC), rSpecT-adjacency (58.0% accuracy, 62.5% AUC), and rSpecT-laplacian (58.8% accuracy, 61.5% AUC). the connectivity patterns visualized using the developed tools revealed distinct differences between methods, offering promising insights for neuroscientific interpretation and potential biomarker discovery.

Automotive radar is an important sensor technology for self-driving cars and Advanced Driver-Assistance Systems (ADAS). Current automotive radars lack the ability to classify and categorize objects due to their limited angular resolution. A new generation of automotive radar systems, known as automotive imaging radars, proposes to overcome this limitation by using larger apertures with more antenna elements. During the radar operation, automotive imaging radar systems face challenges in the accurate estimation of the Direction-of-Arrival (DoA) due to phase incoherency in the spatially sampled information caused by hardware imperfections, temperature variations, and aging effects. This work proposes a method combining convex optimization and alternating updates to first jointly calibrate the phase incoherencies and estimate the DoAs, and then update them iteratively. It further derives the Cramér-Rao Bound (CRB) and investigates the impact of the phase incoherency on DoA estimation using the CRB. In the proposed approach, the MUltiple SIgnal Classification (MUSIC) algorithm is applied to estimate the DoAs after each calibration. Additionally, the eigenvalue decomposition process in MUSIC is replaced by the Projection Approximation Subspace Tracking (PAST) algorithm to reduce computational complexity while maintaining the accuracy of DoA estimation. Experimental results illustrate the effectiveness of these techniques, highlighting their potential in improving next-generation automotive radar systems.

While the success of improving direction of arrival (DOA) estimation with linear coded covers using a single acoustic vector sensors (AVS) has been established, the extension of this theory to arraybased systems remains unexplored. To address this gap, we employ a specially designed coded cover and leverage compressed sensing (CS) and compressed covariance sensing (CCS) methods, extending their application from single AVS systems to an array-based acoustic measurement system. Our results demonstrate that a 14×10 coded cover with 12 PU probes enables accurate localization of 100 sound sources in 3D, even at a signal to noise ratio (SNR) as low as 10 dB, showcasing the scalability and robustness of this approach. To further enhance localization accuracy, we implement a selfcalibration method in the covariance domain to correct phase and gain errors in each receiving channel. Additionally, we combine selfcalibration with CCS to improve resolution and reduce side lobes. For geometric mismatch, we first investigate the sparsity-cognizant total least-squares (STLS) with multiple measurement vectors (MMV) variant of the fast iterative shrinkage-thresholding algorithm (FISTA) method. Then a grid-searching strategy is employed to compensate for these mismatches, ensuring better estimation accuracy. Experimental validation confirms that these techniques significantly enhance DOA estimation under non-ideal conditions, contributing to the advancement of acoustic sensing and localization methodologies.

Ultrasound is a widely used real-time imaging modality to diagnose patients. Ultrasound imaging has several modes of operation such as ultrafast Doppler which, due to the high frame-rates, is particularly suited to image blood flow inside bodily organs such as the brain. Despite its success, the ultrafast imaging technique has some downsides such as lower overall signal-to-noise ratio (SNR), especially in deeper regions due to the use of unfocussed transmissions. This thesis explores the use of advanced signal processing methods such as model-based image reconstruction to regain some of the loss in SNR.

Chapters 3, 4, 5, and 6 of the thesis focus on advanced model-based image reconstruction techniques, incorporating complex priors or statistical assumptions about the signal and noise instead of using a simple physical propagation model. Conventional ultrasound beamforming techniques, such as the delay-and-sum (DAS) beamformer, perform well in many clinical settings; however, they face challenges in applications requiring high structural detail or SNR, such as vascular imaging. This thesis explores deterministic and statistical model-based vascular image reconstruction techniques to improve SNR, resolution, and clarity of fine vascular details. The proposed techniques exploit the joint sparsity of the vasculature images at different time instants. These methods enhance the depiction of vascular structures while increasing SNR and suppressing background noise and artifacts. A large part of the thesis, including Chapters 4, 5 and 6, focuses on the sparse Bayesian learning (SBL) techniques. Starting with classical SBL, this thesis introduces the application of block-sparsity-based SBL techniques, such as pattern-coupled sparse Bayesian learning with fixed-point iterations and correlated sparse Bayesian learning. Although some of the proposed techniques are not computationally efficient yet for real-time ultrasound imaging, they do provide a new contribution to signal processing and computational imaging fields.

Chapter 7 of the thesis focuses on improving the ultrasound transmission to enhance the SNR. An optimized coded excitation technique has been proposed as an alternative to standard coded excitation techniques. By keeping the computational complexity toa modest level, the codes are optimized to increase the SNR without a significant loss in the image resolution. The Cramér-Rao lower bound (CRB) minimization and a faster alternative Fisher information matrix (FIM) maximization have been proposed to optimize the codes. The optimized codes are tested on simulated data to demonstrate their potential for flow imaging.

To sum up, this thesis contributes to the ultrasound blood flow imaging area through solutions on image reconstruction algorithms and ultrasound transmissions to overcome current limitations and challenges. This thesis explores using advanced modelbased signal processing methods to improve image quality. Therefore, this work contributes new strategies that can inspire future research and clinical applications in vascular ultrasound imaging.

Machine learning has been growing beyond data living on Euclidean spaces (e.g., texts, audios, images). Graph machine learning models, e.g., graph neural networks (GNNs), succeed in learning from graph-structured data using the graph topological information. In this thesis, we focus on a new domain, simplicial complexes. Not only are they a popular higher-order network model that generalizes graph models encoding pairwise relations between nodes, but they also allow us to support signals on various network objects (nodes, edges, and faces). For example, edge flows defined on a simplicial complex can be studied in terms of both divergent and rotational properties, providing a better model for real-world flows like traffic flows, water flows, money flows, etc.
The main theme of the thesis is to develop principled machine learning models for signals on simplicial complexes. By principled, we mean that the models leverage the intrinsic priors of the domain and the signals, namely, the topological structure of simplicial compelxes and the Hodge decomposition of simplicial signals. The latter states that, for example, edge flows can be decomposed into a divergence-free part and a curl-free part, each modeling the distinct properties of real-world flows — the conservation of flows (e.g., water flows) and the rotational properties of flows (e.g., electric currents)....

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.

The rapid development of Advanced Driver Assistance Systems (ADAS) necessitates enhanced performance in automotive radar systems, with Phase Modulated ContinuousWave (PMCW) radar emerging as a key technology due to its high resolution, interference resistance, and robust performance. Despite these advantages, PMCW radar faces challenges such as high computational complexity and Doppler-induced range sidelobes. This thesis addresses these challenges by proposing an adaptive block FFT correlation method to reduce computational complexity and enhance processing efficiency, ensuring reliable target detection. Additionally, we tackle Dopplerinduced range sidelobes by introducing code diversity and novel frame designs for MIMO systems, leveraging cyclic shifts and Hadamard matrices to balance sidelobe attenuation and sequence set size requirements. Through extensive analysis and simulations, the proposed methods demonstrate significant improvements in radar performance, especially in detecting weak targets behind strong reflectors. The findings contribute to developing more efficient, reliable, and scalable PMCW radar systems for advanced automotive applications.

Pursuing higher communication rates is a perpetual goal, especially in today's age of information explosion. To increase line rate without extending the optical and electrical bandwidth, advanced modulation formats such as probabilistic constellation shaping (PCS) and partial response signaling (PRS) have been researched. PCS offers up to 1.53 dB sensitivity gains by modifying the uniform distribution of transmitted symbols into the Maxwell-Boltzmann distribution to approximate a Gaussian distribution; PRS, also known as faster-than-Nyquist signaling, increases the symbol rate beyond the ideal Nyquist bandwidth limit by introducing controlled inter-symbol interference (ISI). However, when applied to PCS-enabled or PRS-enabled systems, digital signal processing (DSP) algorithms developed for conventional QAM with uniform probabilities and free ISIs often perform poorly, degrading the expected gain.

To maximize the benefits of PCS and PRS, thereby enhancing the performance of single-carrier coherent communication systems, this thesis focuses on addressing the problem of optimal degradation in the carrier recovery stage. In coherent optical communication systems, carrier recovery is a crucial DSP subsystem that compensates for time-varying carrier frequency offset and phase noise caused by both lasers at the transmitter and receiver.

We first propose a carrier recovery scheme using generalized maximum likelihood estimation with negligible pilot overhead (approximately 0.2%) in the context of PCS. Through simulations and 100 GBaud experiments with PCS-64QAM, our proposed scheme doubles computational efficiency, provides better estimation accuracy, and exhibits greater stability, leading to up to 0.25 dB sensitivity gain compared to other algorithms. We also determine the practical optimal shaping factors of PCS-64QAM for different SNR intervals to guide future experimental work.

Additionally, in a popular PRS scheme, Tomlinson-Harashima precoding combined with polybinary shaping (THP + Polybinary), we compare two 2M modulo formats and investigate their impact on carrier recovery. Based on simulations and 96 GBaud experiments with THP+Polybinary-16QAM, our carrier recovery scheme enhances both accuracy and stability, effectively mitigating issues caused by zero symbols and residual ISIs.

With its superior overall performance, the proposed carrier recovery scheme is a competitive algorithm for addressing carrier imperfections in both PCS-enabled and PRS-enabled high-speed coherent optical communications. For the future, modifying the timing recovery algorithm and the blind equalization algorithm to suit PCS/PRS systems is prioritized to maximize PCS/PRS gains. Given the vast amount of communication data, machine learning-based DSP algorithms also present an interesting avenue for future research.

Doppler ultrasound imaging of cerebral blood flow faces challenges arising from a low signal-to-noise ratio (SNR) and a wide dynamic range. Echo signals received from blood cells are significantly weaker compared to surrounding tissues, such as the skull or brain soft tissue, resulting in inhibited visualization of small blood vessels and deep brain areas. To address this issue, this thesis explored the feasibility of employing and improving coded excitation techniques to enhance the SNR of Doppler ultrasound images. Furthermore, an optimized code for Doppler ultrasound imaging is designed, represented by a generalized encoding matrix.
The research begins with the definition of a linear signal model that incorporates the encoding matrix. Subsequently, a trace-constraint optimization problem is formulated based on maximizing the Fisher information matrix to find the optimized encoding matrix. The feasibility and performance of the optimized encoding matrix are assessed through simulations on both small and large array settings, which operate above Nyquist sampling frequency and under Nyquist sampling frequency respectively. The imaging results indicate that the optimized code exhibits higher SNR in deep image regions compared to existing coded excitation methods like Barker code while using the same number of transmissions, bit length, and same average transmit energy, albeit with a trade-off of decreased axial resolution. Nonetheless, this resolution degradation can be mitigated through the application of the iterative imaging technique LSQR. Finally, the optimized code is tested in a clinical transducer setting, and a blood flow simulation is conducted. The outcomes showcase the capacity of the proposed optimized code to enable higher SNR in Doppler ultrasound imaging and more accurate and informative clinical assessments.

Ultrasound images are typically generated using the Delay-And-Sum (DAS) method, which assumes a homogeneous propagation medium. When an aberrating layer is situated between the sensor array and the imaging target, this assumption does not hold, and DAS is replaced with model-based methods. These methods are computationally expensive and require to accurately model the aberrations caused by the layer. This thesis investigates novel methods for image formation and aberration estimation. The effect of the layer is described using a set of transfer functions from the sensor array to a virtual array placed after the layer. In the first part, we assume the transfer functions are known, and we propose a new method for image formation. The transfer functions allow to map the signal from the sensor array to the virtual array, and the DAS method is used on the virtual array signal. This technique is equivalent to model-based matched filtering in terms of image quality, without requiring expensive matrix computations. In the second part, the transfer functions are unknown, and a novel technique is introduced for their estimation. Using pulse-echo data, a focus-quality metric is computed to quantify the accuracy of the transfer function estimate. The transfer functions are modeled using a dictionary and the dictionary coefficients are iteratively updated to increase the defined metric. The optimization leads to improved focus quality and sharper images. In the case the layer model requires a limited dictionary, the proposed algorithm generates an accurate estimate of the transfer functions.

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.

Subgraph matching is a fundamental problem in various fields such as machine learning, computer vision, image processing, and bioinformatics, where detecting specific substructures within an object is often crucial. In these domains, not only structure plays an essential role, but also the feature information on nodes should be incorporated, thus highlighting the necessity for comprehensive analytical approaches.

In this thesis, we propose two novel subgraph matching frameworks using the Fused Gromov-Wasserstein (FGW) distance, namely the Subgraph Optimal Transport (SOT) and the Sliding Subgraph Optimal Transport (SSOT). Both frameworks integrate a dummy node strategy to handle the discrepancy between two graphs of different sizes. The SSOT extends upon the SOT by incorporating a sliding window framework and Wasserstein pruning to enhance the performance, especially for sparse large graphs. Our frameworks can be easily implemented and are adaptable for problems of exact matching, top-k approximate matching, and inexact matching.

We further propose a normalized FGW distance to cater to the practical interests and enhance the performance evaluation. We adopt the Frank-Wolfe algorithm for optimization and develop computation-reducing techniques by isolating the dummy node.

By conducting experiments on both synthetic and real-world datasets, we demonstrate that the SOT method achieves excellent performance on small graphs, and the SSOT method improves the accuracy over the SOT on large graphs. Both these two methods show the ability to outperform the state-of-the-art methods in noisy environments in terms of accuracy and efficiency.

This study delves into the application of coded covers in enhancing Acoustic Vector Sensor (AVS) performance for sound source localization. We initially explored the use of a coded mask inspired by ultrasound imaging. However, our analysis indicated that the coded mask primarily acts as a scaling factor without substantial benefits for direction of arrival (DOA) estimation.
In response, we investigated an alternative approach using a larger cover with spaced channels, positioned above the AVS sensor. In this setup, each channel operates independently, and their combined acoustic outputs are analyzed upon reaching the sensor. Importantly, the upper surface channels can be viewed as a virtual uniform linear array (ULA), allowing the application of compressed analysis methods.
Two distinct DOA estimation approaches were developed: the compressive sampling (CS) method and the compressive covariance sensing (CCS) method. Both methods were validated, showing improved accuracy in angle estimation. Notably, the CCS method exhibited the potential to expand the number of detectable sound sources using a single AVS.
In summary, while the coded mask did not offer significant advantages, the coded cover design, along with the CS and CCS methods, improved DOA accuracy and extended the detection capabilities of single AVS.

In recent years, neural networks (NNs) have seen a surge in popularity due to their ability to model complex patterns and relationships in data. One of the challenges of using NNs is the requirement for large amounts of labelled data to train the model effectively. In many real-world applications such as radar, labelled data may be scarce due to the high cost of acquiring measurements together with privacy and security concerns.

To overcome the lack of data, researchers have resorted to data augmentation (DA), a technique that aims to solve the problem at the root by generating new training samples by leveraging the available ones. In computer vision, image transformations and generative networks are used to perform DA. These techniques, however, may lead to the production of physically unfeasible samples that may hinder the generalization capabilities of classifiers in domains where the data has an underlying physical meaning.

Physics-informed machine learning aims to incorporate physical prior knowledge and governing equations of the target domain into the machine learning pipeline to improve the performance of NNs in fields with limited available data but with well-defined physical models. In this thesis, physics-informed DA in the radar domain is addressed to improve the task of classifying armed and unarmed walking individuals through micro-Doppler spectrograms.

To begin with, the usage of model-driven micro-Doppler radar simulations to improve the existing generative augmentations is investigated. After introducing several generative NN architectures, the quality and diversity of the produced synthetic spectrograms are evaluated together with their effect on the downstream classification task.


Next, the impact of visual transformations on micro-Doppler spectrograms is studied. Their effect on the underlying physics of the micro-Doppler spectrograms and their impact on feature extraction is assessed. Based on the results, a new DA technique is devised to improve the feature extraction process by informed segmentation of the input spectrogram, halving the size of the NN model and reducing the risk of overfitting.