Distributed Denoising over Simplicial Complexes using Chebyshev Polynomial Approximation

Kadambari, SK and Francis, R and Chepuri, SP (2022) Distributed Denoising over Simplicial Complexes using Chebyshev Polynomial Approximation. In: 30th European Signal Processing Conference, EUSIPCO 2022, 29 August - 2 September 2022, Belgrade, pp. 822-826.

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Abstract

In this work, we focus on denoising smooth signals supported on simplicial complexes in a distributed manner. We assume that the simplicial signals are dominantly smooth on either the lower or upper Laplacian matrices, which are used to compose the so-called Hodge Laplacian matrix. This corresponds to denoising non-harmonic signals on simplicial complexes. We pose the denoising problem as a convex optimization problem, where we assign different weights to the quadratic regularizers related to the upper and lower Hodge Laplacian matrices and express the optimal solution as a sum of simplicial complex operators related to the two Laplacian matrices. We then use the recursive relation of the Chebyshev polynomial to implement these operators in a distributed manner. We demonstrate the efficacy of the developed framework on synthetic and real-world datasets.

Item Type:	Conference Paper
Publication:	European Signal Processing Conference
Publisher:	European Signal Processing Conference, EUSIPCO
Additional Information:	The copyright for this article belongs to European Signal Processing Conference, EUSIPCO.
Keywords:	Convex optimization; Laplace transforms; Matrix algebra; Polynomial approximation; Signal denoising, Chebyshev polynomials; Chebyshev polynomials approximation; De-noising; Denoising problems; Distributed signal processing; Harmonic signals; Hodge Laplacian; Laplacian matrices; Signal-on; Simplicial complex, Chebyshev polynomials
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	22 Nov 2022 05:40
Last Modified:	22 Nov 2022 05:40
URI:	https://eprints.iisc.ac.in/id/eprint/77904

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