Related papers: Fractional spectral graph wavelets and their appli…
The analysis of multi-dimensional graph signals on complex structured domains remains a fundamental challenge,
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
In Graph Signal Processing (GSP), data dependencies are represented by a graph whose nodes label the data and the edges capture dependencies among nodes. The graph is represented by a weighted adjacency matrix $A$ that, in GSP, generalizes…
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…
The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…
Spectral graph convolution, an important tool of data filtering on graphs, relies on two essential decisions: selecting spectral bases for signal transformation and parameterizing the kernel for frequency analysis. While recent techniques…
Inspired by the success of foundation models in applications such as ChatGPT, as graph data has been ubiquitous, one can envision the far-reaching impacts that can be brought by Graph Foundation Models (GFMs) with broader applications in…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet…
In the past decade, several multi-resolution representation theories for graph signals have been proposed. Bipartite filter-banks stand out as the most natural extension of time domain filter-banks, in part because perfect reconstruction,…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
This paper proposes a graph linear canonical transform (GLCT) by decomposing the linear canonical parameter matrix into fractional Fourier transform, scale transform, and chirp modulation for graph signal processing. The GLCT enables…
Graph signal processing, like the graph Fourier transform, requires the full graph signal at every vertex of the graph. However, in practice, only signals at a subset of vertices may be available. We propose a subgraph signal processing…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…