Browsing by Subject "Graph signal processing (GSP)"
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Item Open Access Graph signal processing: Vertex multiplication(IEEE, 2021-06-03) Kartal, Bünyamin; Bayiz, Y. E.; Koç, AykutOn the Euclidean domains of classical signal processing, linking of signal samples to underlying coordinate structures is straightforward. While graph adjacency matrices totally define the quantitative associations among the underlying graph vertices, a major problem in graph signal processing is the lack of explicit association of vertices with an underlying coordinate structure. To make this link, we propose an operation, called the vertex multiplication (VM), which is defined for graphs and can operate on graph signals. VM, which generalizes the coordinate multiplication (CM) operation in time series signals, can be interpreted as an operator that assigns a coordinate structure to a graph. By using the graph domain extension of differentiation and graph Fourier transform (GFT), VM is defined such that it shows Fourier duality that differentiation and CM operations are duals of each other under Fourier transformation (FT). Numerical examples and applications are also presented.Item Open Access Optimal fractional fourier filtering for graph signals(IEEE, 2021-05-19) Öztürk, Cüneyd; Özaktaş, Haldun M.; Gezici, Sinan; Koç, AykutGraph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.Item Open Access RadGT: graph and transformer-based automotive radar point cloud segmentation(Institute of Electrical and Electronics Engineers, 2023-10-25) Sevimli, R. A.; Ucuncu, M.; Koç, AykutThe need for visual perception systems providing situational awareness to autonomous vehicles has grown significantly. While traditional deep neural networks are effective for solving 2-D Euclidean problems, point cloud analysis, particularly for radar data, contains unique challenges because of the irregular geometry of point clouds. This letter proposes a novel transformer-based architecture for radar point clouds adapted to the graph signal processing (GSP) framework, designed to handle non-Euclidean and irregular signal structures. We provide experimental results by using well-established benchmarks on the nuScenes and RadarScenes datasets to validate our proposed method.