Related papers: Chebyshev Polynomial Approximation for Distributed…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
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…
In this paper we analyze the use of Chebyshev polynomials in distributed consensus applications. We study the properties of these polynomials to propose a distributed algorithm that reaches the consensus in a fast way. The algorithm is…
Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…
Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…
Diffusing a graph signal at multiple scales requires computing the action of the exponential of several multiples of the Laplacian matrix. We tighten a bound on the approximation error of truncated Chebyshev polynomial approximations of the…
Polynomial graph filters and their inverses play important roles in graph signal processing. An advantage of polynomial graph filters is that they can be implemented in a distributed manner, which involves data transmission between adjacent…
Graph propagation (GP) computation plays a crucial role in graph data analysis, supporting various applications such as graph node similarity queries, graph node ranking, graph clustering, and graph neural networks. Existing methods, mainly…
In 3D image/video acquisition, different views are often captured with varying noise levels across the views. In this paper, we propose a graph-based image enhancement technique that uses a higher quality view to enhance a degraded view. A…
We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…
We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to…
Graph signal processing is a framework to handle graph structured data. The fundamental concept is graph shift operator, giving rise to the graph Fourier transform. While the graph Fourier transform is a centralized procedure, distributed…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…
Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to…
We propose a framework for the derivation and evaluation of distributed iterative algorithms for receiver cooperation in interference-limited wireless systems. Our approach views the processing within and collaboration between receivers as…