Direction of arrival estimation based on information geometry

In this paper, a new direction of arrival (DOA) estimation approach is devised using concepts from information geometry (IG). The proposed method uses geodesic distances in the statistical manifold of probability distributions parametrized by their covariance matrix to estimate the direction of arrival of several sources. In order to obtain a practical method, the DOA estimation is treated as a single-variable optimization problem, for which the DOA solutions are found by means of a line search. The relation between the proposed method and MVDR beamformer is elucidated. An evaluation of its performance is carried out by means of Monte Carlo simulations and it is shown that the proposed method provides improved resolution capabilities at low SNR with respect to MUSIC and MVDR.Accepted Author ManuscriptCircuits and System

Advances in graph signal processing: Graph filtering and network identification

To the surprise of most of us, complexity in nature spawns from simplicity. No matter how simple a basic unit is, when many of them work together, the interactions among these units lead to complexity. This complexity is present in the spreading of diseases, where slightly different policies, or conditions,might lead to very different results; or in biological systems where the interactions between elements maintain the delicate balance that keep life running. Fortunately, despite their complexity, current advances in technology have allowed us to have more than just a sneak-peak at these systems. With new views on how to observe such systems and gather data, we aimto understand the complexity within.One of these new views comes from the field of graph signal processing which provides models and tools to understand and process data coming from such complex systems. With a principled view, coming from its signal processing background, graph signal processing establishes the basis for addressing problems involving data defined over interconnected systems by combining knowledge from graph and network theory with signal processing tools. In this thesis, our goal is to advance the current state-of-the-art by studying the processing of network data using graph filters, the workhorse of graph signal processing, and by proposing methods for identifying the topology (interactions) of a network from network measurements.To extend the capabilities of current graph filters, the network-domain counterparts of time-domain filters, we introduce a generalization of graph filters. This new family of filters does not only provide more flexibility in terms of processing networked data distributively but also reduces the communications in typical network applications, such as distributed consensus or beamforming. Furthermore, we theoretically characterize these generalized graph filters and also propose a practical and numerically-amenable cascaded implementation.As allmethods in graph signal processingmake use of the structure of the network, we require to know the topology. Therefore, identifying the network interconnections from networked data is much needed for appropriately processing this data. In this thesis, we pose the network topology identification problem through the lens of system identification and study the effect of collecting information only from part of the elements of the network. We show that by using the state-space formalism, algebraic methods can be applied to the network identification problem successfully. Further, we demonstrate that for the partially-observable case, although ambiguities arise, we can still retrieve a coherent network topology leveraging state-of-the-art optimization techniques.Circuits and System

A Cascaded Structure for Generalized Graph Filters

One of the main challenges of graph filters is the stability of their design. While classical graph filters allow for a stable design using optimal polynomial approximation theory, generalized graph filters tend to suffer from the ill-conditioning of the involved system matrix. This issue, accentuated for increasing graph filter orders, naturally leads to very large (small) filter coefficients or error saturation, casting a shadow on the benefits of these richer graph filter structures. In addition to this, data-driven design/learning of graph filters with large filter orders, even in the case of classical graph filters, suffers from the eigenvalue spread of the input data covariance matrix and mode coupling, leading to convergence-related issues as the ones observed when identifying time-domain filters with large orders. To alleviate these conditioning and convergence problems, and to reduce the overall design complexity, in this work, we propose a cascaded implementation of generalized graph filters and an efficient algorithm for designing the graph filter coefficients in both model- and data-driven settings. Further, we establish the connections of this implementation with so-called graph convolutional neural networks and demonstrate the performance of the proposed structure in different network applications. By the proposed approach, further error reduction and better design stability are achieved.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care   Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Signal Processing System

Asynchronous Distributed Edge-Variant Graph Filters

As the size of the sensor network grows, synchronization starts to become the main bottleneck for distributed computing. As a result, efforts in several areas have been focused on the convergence analysis of asynchronous computational methods. In this work, we aim to cross-pollinate distributed graph filters with results in parallel computing to provide guarantees for asynchronous graph filtering. To alleviate the possible reduction of convergence speed due to asynchronous updates, we also show how a slight modification to the graph filter recursion, through operator splitting, can be performed to obtain faster convergence. Finally, through numerical experiments the performance of the discussed methods is illustrated.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System

Bound on the estimation grid size for sparse reconstruction in direction of arrival estimation

A bound for sparse reconstruction involving both the signal-to-noise ratio (SNR) and the estimation grid size is presented. The bound is illustrated for the case of a uniform linear array (ULA). By reducing the number of possible sparse vectors present in the feasible set of a constrained ℓ1-norm minimization problem, ambiguities in the reconstruction of a single source under noise can be reduced. This reduction is achieved by means of a proper selection of the estimation grid, which is naturally linked with the mutual coherence of the sensing matrix. Numerical simulations show the performance of sparse reconstruction with an estimation grid meeting the provided bound demonstrating the effectiveness of the proposed bound.Circuits and System

Subset Selection for Kernel-Based Signal Reconstruction

In this work, we introduce subset selection strategies for signal reconstruction based on kernel methods, particularly for the case of kernel-ridge regression. Typically, these methods are employed for exploiting known prior information about the structure of the signal of interest. We use the mean squared error and a scalar function of the covariance matrix of the kernel regressors to establish metrics for the subset selection problem. Despite the NP-hard nature of the problem, we introduce efficient algorithms for finding approximate solutions for the proposed metrics. Finally, numerical experiments demonstrate the applicability of the proposed strategies.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System

Advances in Distributed Graph Filtering

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this paper generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize a subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parameterization, these shift-invariant filters provide new insights in approximating linear graph spectral operators through the succession and composition of local operators, i.e., fixed support matrices. A set of numerical results shows the benefits of the edge-variant graph filters over current methods and illustrates their potential to a wider range of applications than graph filtering.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System

Sparse sensing for composite matched subspace detection

In this paper, we propose sensor selection strategies, based on convex and greedy approaches, for designing sparse samplers for composite detection. Particularly, we focus our attention on sparse samplers for matched subspace detectors. Differently from previous works, that mostly rely on random matrices to perform compression of the sub-spaces, we show how deterministic samplers can be designed under a Neyman-Pearson-like setting when the generalized likelihood ratio test is used. For a less stringent case than the worst case design, we introduce a submodular cost that obtains comparable results with its convex counterpart, while having a linear time heuristic for its near optimal maximization.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System

Sparsest Network Support Estimation: A Submodular Approach

In this work, we address the problem of identifying the underlying network structure of data. Different from other approaches, which are mainly based on convex relaxations of an integer problem, here we take a distinct route relying on algebraic properties of a matrix representation of the network. By describing what we call possible ambiguities on the network topology, we proceed to employ sub-modular analysis techniques for retrieving the network support, i.e., network edges. To achieve this we only make use of the network modes derived from the data. Numerical examples showcase the effectiveness of the proposed algorithm in recovering the support of sparse networks.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System

Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes

Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in this paper, we focus on the joint identification of coefficients and graph weights defining the graph filter that best models the observed input/output network data. While these two problems have been mostly addressed separately, we here propose an iterative method that exploits the knowledge of the support of the graph for the joint identification of graph filter coefficients and edge weights. We further show that our iterative scheme guarantees a non-increasing cost at every iteration, ensuring a globally-convergent behavior. Numerical experiments confirm the applicability of our proposed approach.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Circuits and System