Related papers: Graph-Based Manifold Frequency Analysis for Denois…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based…
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…
With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of…
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the…
Directed acyclic graphs (DAGs) are used for modeling causal relationships, dependencies, and flows in various systems. However, spectral analysis becomes impractical in this setting because the eigendecomposition of the adjacency matrix…
The graph Laplacian is an important tool in Graph Signal Processing (GSP) as its eigenvalue decomposition acts as an analogue to the Fourier transform and is known as the Graph Fourier Transform (GFT). The line graph has a GFT that is a…
Dynamic graph signal processing provides a principled framework for analyzing time-varying data defined on irregular graph domains. However, existing joint time-vertex transforms such as the joint time-vertex fractional Fourier transform…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…
Wiener filtering in the joint time-vertex fractional Fourier transform (JFRFT) domain has shown high effectiveness in denoising time-varying graph signals. Traditional filtering models use grid search to determine the transform-order pair…
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 this work, we provide a theoretical understanding of the framelet-based graph neural networks through the perspective of energy gradient flow. By viewing the framelet-based models as discretized gradient flows of some energy, we show it…
With the proliferation of sophisticated cameras in modern society, the demand for accurate and visually pleasing images is increasing. However, the quality of an image captured by a camera may be degraded by noise. Thus, some processing of…
The depth images denoising are increasingly becoming the hot research topic nowadays because they reflect the three-dimensional (3D) scene and can be applied in various fields of computer vision. But the depth images obtained from depth…
Accurately predicting long-horizon molecular dynamics (MD) trajectories remains a significant challenge, as existing deep learning methods often struggle to retain fidelity over extended simulations. We hypothesize that one key factor…
Our goal in this paper is the robust design of filters acting on signals observed over graphs subject to small perturbations of their edges. The focus is on developing a method to identify spectral and polynomial graph filters that can…
Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs…
In wireless communications, recovering the optimal solution to the multiple-input multiple-output (MIMO) detection problem is NP-hard. Obtaining high-quality suboptimal solutions with a favorable performance-complexity trade-off is…
To improve the performance in identifying the faults under strong noise for rotating machinery, this paper presents a dynamic feature reconstruction signal graph method, which plays the key role of the proposed end-to-end fault diagnosis…