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Forecasting Graph Signals with Recursive MIMO Graph Filters

van der Hoeven, Jelmer (author), Natali, A. (author), Leus, G.J.T. (author)

Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product graphs to combine this multidimensional information, at the expense of creating a larger graph. In this...

conference paper 2023

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Sensor Selection for Angle of Arrival Estimation Based on the Two-Target Cramér-Rao Bound

Kokke, C.A. (author), Coutino, Mario (author), Anitori, Laura (author), Heusdens, R. (author), Leus, G.J.T. (author)

Sensor selection is a useful method to help reduce data throughput, as well as computational, power, and hardware requirements, while still maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown source models. In this work, we...

conference paper 2023

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Robust Pareto-Optimal Radar Receive Filter Design for Noise and Sidelobe Suppression

Kokke, C.A. (author), Coutiño, Mario (author), Heusdens, R. (author), Leus, G.J.T. (author), Anitori, Laura (author)

Integrated sidelobe level is a useful measure to quantify robustness of a waveform-filter pair to unknown range clutter and multiple closely located targets. Sidelobe suppression on receive will incur a loss in the signal to noise ratio after pulse compression. We derive a pulse compression filter that has the greatest integrated sidelobe...

conference paper 2023

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Array Design Based on the Worst-Case Cramér-Rao Bound to Account for Multiple Targets

Kokke, C.A. (author), Coutino, Mario (author), Heusdens, R. (author), Leus, G.J.T. (author)

Sensor selection is a useful method to help reduce computational, hardware, and power requirements while maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions. We propose to tackle the sensor selection problem...

conference paper 2023

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Single-Pulse Estimation of Target Velocity on Planar Arrays

Kokke, C.A. (author), Coutino, Mario (author), Heusdens, R. (author), Leus, G.J.T. (author), Anitori, L. (author)

Doppler velocity estimation in pulse-Doppler radar is done by evaluating the target returns of bursts of pulses. While this provides convenience and accuracy, it requires multiple pulses. In adaptive and cognitive radar systems, the ability to adapt on consecutive pulses, instead of bursts, brings potential performance benefits. Hence, with...

conference paper 2022

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Topological Volterra Filters

Leus, G.J.T. (author), Yang, Maosheng (author), Coutino, Mario (author), Isufi, E. (author)

To deal with high-dimensional data, graph filters have shown their power in both graph signal processing and data science. However, graph filters process signals exploiting only pairwise interactions between the nodes, and they are not able to exploit more complicated topological structures. Graph Volterra models, on the other hand, are also...

conference paper 2021

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Online Graph Learning From Time-Varying Structural Equation Models

Natali, A. (author), Isufi, E. (author), Coutino, Mario (author), Leus, G.J.T. (author)

Topology identification is an important problem across many disciplines, since it reveals pairwise interactions among entities and can be used to interpret graph data. In many scenarios, however, this (unknown) topology is time-varying, rendering the problem even harder. In this paper, we focus on a time-varying version of the structural...

conference paper 2021

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Finite Impulse Response Filters for Simplicial Complexes

Yang, Maosheng (author), Isufi, E. (author), Schaub, Michael T. (author), Leus, G.J.T. (author)

In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be...

conference paper 2021

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State-space based network topology identification

Coutino, Mario (author), Isufi, E. (author), Maehara, T. (author), Leus, G.J.T. (author)

In this work, we explore the state-space formulation of network processes to recover the underlying network structure (local connections). To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology inference problem. This approach provides a unified view of the traditional...

conference paper 2020

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Privacy-Preserving Distributed Graph Filtering

Li, Qiongxiu (author), Coutino, Mario (author), Leus, G.J.T. (author), Christensen, M. Graesboll (author)

With an increasingly interconnected and digitized world, distributed signal processing and graph signal processing have been proposed to process its big amount of data. However, privacy has become one of the biggest challenges holding back the widespread adoption of these tools for processing sensitive data. As a step towards a solution, we...

conference paper 2020

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Vector Doppler imaging of small vessels using directionally filtered Power Doppler images

Generowicz, B.S. (author), Verhoef, Luuk (author), Mastik, Frits (author), Dijkhuizen, Stefanie (author), van Dorp, Nikki (author), Voorneveld, Jason (author), Bosch, Johannes (author), Kumar, Karishma (author), Leus, G.J.T. (author)

Power Doppler (PD) imaging has become a staple in high frame rate ultrasound imaging due to its ability to image small vessels and slow-moving flows, such as in the case of imaging blood flow in the brain. Alternatively, color Doppler (CD) can be used to determine the one-dimensional directional information of the blood scatterers. This can help...

conference paper 2020

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Forecasting Multi-Dimensional Processes Over Graphs

Natali, A. (author), Isufi, E. (author), Leus, G.J.T. (author)

The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To tackle this issue, we devise a new framework and...

conference paper 2020

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Node varying regularization for graph signals

Yang, M. (author), Coutino, Mario (author), Isufi, E. (author), Leus, G.J.T. (author)

While regularization on graphs has been successful for signal reconstruction, strategies for controlling the bias-variance trade-off of such methods have not been completely explored. In this work, we put forth a node varying regularizer for graph signal reconstruction and develop a minmax approach to design the vector of regularization...

conference paper 2020

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

Natali, A. (author), Coutino, Mario (author), Leus, G.J.T. (author)

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...

conference paper 2020

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Convolutional Graph Neural Networks

Gama, Fernando (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)

Convolutional neural networks (CNNs) restrict the, otherwise arbitrary, linear operation of neural networks to be a convolution with a bank of learned filters. This makes them suitable for learning tasks based on data that exhibit the regular structure of time signals and images. The use of convolutions, however, makes them unsuitable for...

conference paper 2019

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CNN architectures for GRAPH data

Gama, F. (author), Marques, Antonio G. (author), Leus, G.J.T. (author), Ribeiro, Alejandro (author)

In this ongoing work, we describe several architectures that generalize convolutional neural networks (CNNs) to process signals supported on graphs. The general idea of the replace time invariant filters with graph filters to generate convolutional features and to replace pooling with sampling schemes for graph signals. The different...

conference paper 2019

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On the Limits of Finite-Time Distributed Consensus Through Successive Local Linear Operations

Coutino, Mario (author), Isufi, E. (author), Maehara, Takanori (author), Leus, G.J.T. (author)

In this work, we explore the limits of finite-time distributed consensus through the intersection of graph filters and matrix function theory. We focus on algorithms capable to compute the consensus exactly through filtering operations over a graph, and that have been proven to converge in finite time. In this context, we show that there...

conference paper 2019

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Aggregation Graph Neural Networks

Gama, F. (author), Marques, Antonio G. (author), Ribeiro, Alejandro (author), Leus, G.J.T. (author)

Graph neural networks (GNNs) regularize classical neural networks by exploiting the underlying irregular structure supporting graph data, extending its application to broader data domains. The aggregation GNN presented here is a novel GNN that exploits the fact that the data collected at a single node by means of successive local exchanges...

conference paper 2019

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Asynchronous Distributed Edge-Variant Graph Filters

Coutino, Mario (author), Leus, G.J.T. (author)

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...

conference paper 2019

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Distributed edge-variant graph filters

Coutino, Mario (author), Isufi, E. (author), Leus, G.J.T. (author)

The main challenges distributed graph filters face in practice are the communication overhead and computational complexity. In this work, we extend the state-of-the-art distributed finite impulse response (FIR) graph filters to an edge-variant (EV) version, i.e., a filter where every node weights the signals from its neighbors with different...

conference paper 2018