Related papers: Graph Fractional Hilbert Transform: Theory and App…
In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in…
Graph Transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to…
Classical Graph Signal Processing (GSP) provides a robust framework for analyzing signals on irregular domains, utilizing the graph Fourier transform as a cornerstone for spectral analysis and filtering. However, as data structures grow in…
We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely…
A novel addition to the family of integral transforms, the quadratic phase Fourier transform (QPFT) embodies a variety of signal processing tools, including the Fourier transform (FT), fractional Fourier transform (FRFT), linear canonical…
Extending computational harmonic analysis tools from the classical setting of regular lattices to the more general setting of graphs and networks is very important and much research has been done recently. The Generalized Haar-Walsh…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
Spectral graph neural networks learn graph filters, but their behavior with increasing depth and polynomial order is not well understood. We analyze these models in the graph Fourier domain, where each layer becomes an element-wise…
In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and…
Functional connectivity (FC) as derived from fMRI has emerged as a pivotal tool in elucidating the intricacies of various psychiatric disorders and delineating the neural pathways that underpin cognitive and behavioral dynamics inherent to…
An improved phase retrieval method based Hilbert transform is introduced to quantitatively calculate the phase distribution from distorted fringe pattern. Also phase measurement deflectomety are widely used in specular type samples. The…
As a variant of Graph Neural Networks (GNNs), Unfolded GNNs offer enhanced interpretability and flexibility over traditional designs. Nevertheless, they still suffer from scalability challenges when it comes to the training cost. Although…
We propose a new point of view in the study of Fourier analysis on graphs, taking advantage of localization in the Fourier domain. For a signal $f$ on vertices of a weighted graph $\mathcal{G}$ with Laplacian matrix $\mathcal{L}$, standard…
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like…
Graph neural networks (GNNs) have achieved remarkable success in various domains, yet they often struggle with domain adaptation due to significant structural distribution shifts and insufficient exploration of transferable patterns. One of…
We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…
The Hilbert Huang Transform is a new technique for the analysis of non--stationary signals. It comprises two distinct parts: Empirical Mode Decomposition (EMD) and the Hilbert Transform of each of the modes found from the first step to…
Near-field radiative heat transfer (NFRHT) is strongly related with many applications such as near-field imaging, thermos-photovoltaics and thermal circuit devices. The active control of NFRHT is of great interest since it provides a degree…
The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly…