相关论文: Sampling Theory with Average Values on the Sierpin…
The study of sampling signals on graphs, with the goal of building an analog of sampling for standard signals in the time and spatial domains, has attracted considerable attention recently. Beyond adding to the growing theory on graph…
Sampling methods for graph signals in the graph spectral domain are presented. Though conventional sampling of graph signals can be regarded as sampling in the graph vertex domain, it does not have the desired characteristics in regard to…
Using the method of spectral decimation and a modified version of Kirchhoff's Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely…
On the unit interval (I), and the Sierpinski Gasket ($\mathcal{SG}$), the spectral decimation function of the Laplacian has similar properties that result in positive minimum spacing of eigenvalues. Other fractals, for example the level-3…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
Using the method of spectral decimation and a modified version of Kirchhoffs Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. It has a wide spectrum of applications, e.g. survey hidden population in sociology [54], visualize social graph [29], scale down Internet AS graph…
In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\'nski Gasket (SG). We also provide some results related to constrained approximation…
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs…
We present a theoretical framework for analyzing spatial sampling of fields in three-dimensional space. The framework bridges Shannon's sampling and information theory to Bayesian probabilistic inference and experimental design. Based on…
We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…
In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs $\hat C$. This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals. For a…
In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First we show the poor convergence of classical Shannon sampling sums by presenting sharp upper and lower bounds of the norm of the Shannon sampling…
The fast reconstruction of a bandlimited function from its sample data is an essential problem in signal processing. In this paper, we consider the widely used Gaussian regularized Shannon sampling formula in comparison to regularized…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
We prove a general theorem on cutoffs for symmetric simple exclusion processes on graphs with open boundaries, under the natural assumption that the graphs converge geometrically and spectrally to a compact metric measure space with…
Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…
The {\it Sierpi\'nski fractal} or {\it Sierpi\'nski gasket} $\Sigma$ is a familiar object studied by specialists in dynamical systems and probability. In this paper, we consider a graph $S_n$ derived from the first $n$ iterations of the…
This study presents a novel algorithm based on graph theory for the precise segmentation and measurement of detonation cells from 3D pressure traces, termed detonation lattices, addressing the limitations of manual and primitive 2D edge…