Discrete Laplacian Operator and Its Applications in Signal Processing

Fractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the fractional-order operators have numerous definiti...

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Main Authors: Waseem Waheed, Guang Deng, Bo Liu
Format: Article
Language:English
Published: IEEE 2020-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/9090865/
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spelling doaj-cb6e0700c55a4971999372bed36113512021-03-30T01:53:16ZengIEEEIEEE Access2169-35362020-01-018896928970710.1109/ACCESS.2020.29935779090865Discrete Laplacian Operator and Its Applications in Signal ProcessingWaseem Waheed0https://orcid.org/0000-0002-5858-5836Guang Deng1Bo Liu2Department of Engineering, La Trobe University, Melbourne, VIC, AustraliaDepartment of Engineering, La Trobe University, Melbourne, VIC, AustraliaSchool of Computer Science, University of Technology Sydney, Ultimo, NSW, AustraliaFractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the fractional-order operators have numerous definitions. Furthermore, a consensus on the most suitable definition for a given task is yet to be reached. Fractional operators are defined as continuous operators and their implementation requires a discretization step. In this article, we propose a discrete fractional Laplacian as a matrix operator. The proposed operator is real (non-complex) which makes it computationally efficient. The construction of the proposed fractional Laplacian utilizes the DCT transform avoiding the complexity associated with the discretization step which is typical in the constructions based on signal processing. We demonstrate the utility of the proposed operator on a number of data modeling and image processing tasks.https://ieeexplore.ieee.org/document/9090865/Fractional-Laplaciandiscrete operatorimage-processingtrend-filteringfractional calculus
collection DOAJ
language English
format Article
sources DOAJ
author Waseem Waheed
Guang Deng
Bo Liu
spellingShingle Waseem Waheed
Guang Deng
Bo Liu
Discrete Laplacian Operator and Its Applications in Signal Processing
IEEE Access
Fractional-Laplacian
discrete operator
image-processing
trend-filtering
fractional calculus
author_facet Waseem Waheed
Guang Deng
Bo Liu
author_sort Waseem Waheed
title Discrete Laplacian Operator and Its Applications in Signal Processing
title_short Discrete Laplacian Operator and Its Applications in Signal Processing
title_full Discrete Laplacian Operator and Its Applications in Signal Processing
title_fullStr Discrete Laplacian Operator and Its Applications in Signal Processing
title_full_unstemmed Discrete Laplacian Operator and Its Applications in Signal Processing
title_sort discrete laplacian operator and its applications in signal processing
publisher IEEE
series IEEE Access
issn 2169-3536
publishDate 2020-01-01
description Fractional calculus has increased in popularity in recent years, as the number of its applications in different fields has increased. Compared to the traditional operations in calculus (integration and differentiation) which are uniquely defined, the fractional-order operators have numerous definitions. Furthermore, a consensus on the most suitable definition for a given task is yet to be reached. Fractional operators are defined as continuous operators and their implementation requires a discretization step. In this article, we propose a discrete fractional Laplacian as a matrix operator. The proposed operator is real (non-complex) which makes it computationally efficient. The construction of the proposed fractional Laplacian utilizes the DCT transform avoiding the complexity associated with the discretization step which is typical in the constructions based on signal processing. We demonstrate the utility of the proposed operator on a number of data modeling and image processing tasks.
topic Fractional-Laplacian
discrete operator
image-processing
trend-filtering
fractional calculus
url https://ieeexplore.ieee.org/document/9090865/
work_keys_str_mv AT waseemwaheed discretelaplacianoperatoranditsapplicationsinsignalprocessing
AT guangdeng discretelaplacianoperatoranditsapplicationsinsignalprocessing
AT boliu discretelaplacianoperatoranditsapplicationsinsignalprocessing
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