Browsing by Subject "Graph signal processing (GSP)"

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    Graph fractional Fourier transform
    (2024-09) Alikaşifoğlu, Tuna
    The fractional Fourier transform (FRFT) parametrically generalizes the Fourier transform (FT) by a transform order, representing signals in intermediate time-frequency domains. The FRFT has multiple but equivalent definitions each offering benefits like derivational ease and computational efficiency. Concurrently, graph signal processing (GSP) extends traditional signal processing to irregular graph structures, enabling concepts like sampling, filtering, and Fourier transform for graph signals. The graph fractional Fourier transform (GFRFT) is recently extended to the GSP domain. However, this extension only generalizes one definition of FRFT based on specific graph structure with limited transform order range. Ideally, the GFRFT extension should be consistent with as many alternative definitions as possible. This work introduces a unified framework for GFRFT that supports multiple definitions with any graph structure and transform order. The proposed approach also allows faster transform matrix computations on large graphs and learnable transform order. Additionally, data sources on each vertex can also continually provide time-series signals such that graph signals are time varying. Joint time-vertex Fourier transform (JFT), with the associated framework of joint time-vertex (JTV) processing, provides spectral analysis tools for such signals. Just as the FRFT generalizes FT, we propose the joint time-vertex fractional Fourier transform (JFRFT) to generalize JFT. JFRFT provides an additional fractional analysis tool for JTV processing by extending temporal and vertex domains to fractional orders. Recently, the classical optimal Wiener filtering problem is introduced to JTV domain. However, the ordinary Fourier domain is not always optimal for separating the signal and noise; one can reach the smaller error in a fractional domain. We generalize the optimal Wiener filtering to the proposed JFRFT domains and provide a theoretical analysis and solution to the problem in the fractional JTV domains. We numerically verify our claims by presenting computational cost analysis and experiments with comprehensive comparisons to state-of-the-art approaches.
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    Graph signal processing: Vertex multiplication
    (IEEE, 2021-06-03) Kartal, Bünyamin; Bayiz, Y. E.; Koç, Aykut
    On 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.
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    Optimal fractional fourier filtering for graph signals
    (IEEE, 2021-05-19) Öztürk, Cüneyd; Özaktaş, Haldun M.; Gezici, Sinan; Koç, Aykut
    Graph 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.
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    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, Aykut
    The 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.