Related papers: Sparse Representation on Graphs by Tight Wavelet F…
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing…
The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…
We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size $M$, which…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
Given a neighborhood graph representation of a finite set of points $x_i\in\mathbb{R}^d,i=1,\ldots,n,$ we construct a frame (redundant dictionary) for the space of real-valued functions defined on the graph. This frame is adapted to the…
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…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Nonstationary signals are commonly analyzed and processed in the time-frequency (T-F) domain that is obtained by the discrete Gabor transform (DGT). The T-F representation obtained by DGT is spread due to windowing, which may degrade the…
Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…
We investigate the use of wavelet-space feature decomposition in neural super-resolution for rendering pipelines. Building on recent neural upscaling frameworks, we introduce a formulation that predicts stationary wavelet coefficients…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…
Recently, transformers have shown promising performance in learning graph representations. However, there are still some challenges when applying transformers to real-world scenarios due to the fact that deep transformers are hard to train…
Recently, graph prompt learning has garnered increasing attention in adapting pre-trained GNN models for downstream graph learning tasks. However, existing works generally conduct prompting over all graph elements (e.g., nodes, edges, node…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round…
Full waveform inversion (FWI) delivers high-resolution images of the subsurface by minimizing iteratively the misfit between the recorded and calculated seismic data. It has been attacked successfully with the Gauss-Newton method and…
We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform.…