Related papers: Perfect Reconstruction Two-Channel Wavelet Filter-…
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…
In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame…
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…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and…
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space…
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…
We introduce a multi-windowed graph Fourier transform (MWGFT) for the joint vertex-frequency analysis of signals defined on graphs. Building on generalized translation and modulation induced by the graph Laplacian, the proposed framework…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…
The shift operation plays a crucial role in the classical signal processing. It is the generator of all the filters and the basic operation for time-frequency analysis, such as windowed Fourier transform and wavelet transform. With the…
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…
We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian…
Key to successfully deal with complex contemporary datasets is the development of tractable models that account for the irregular structure of the information at hand. This paper provides a comprehensive and unifying view of several…
Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth,…
In this paper, we consider Wiener filters to reconstruct deterministic and (wide-band) stationary graph signals from their observations corrupted by random noises, and we propose distributed algorithms to implement Wiener filters and…
We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the…