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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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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1724186259815923712 |