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The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †

Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between th...

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Detalles Bibliográficos
Autores principales: Pan, Chao, Lv, Zhicheng, Hua, Xia, Li, Hongyan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7085734/
https://www.ncbi.nlm.nih.gov/pubmed/32121475
http://dx.doi.org/10.3390/s20051353
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author Pan, Chao
Lv, Zhicheng
Hua, Xia
Li, Hongyan
author_facet Pan, Chao
Lv, Zhicheng
Hua, Xia
Li, Hongyan
author_sort Pan, Chao
collection PubMed
description Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.
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spelling pubmed-70857342020-03-25 The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment † Pan, Chao Lv, Zhicheng Hua, Xia Li, Hongyan Sensors (Basel) Article Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method. MDPI 2020-03-01 /pmc/articles/PMC7085734/ /pubmed/32121475 http://dx.doi.org/10.3390/s20051353 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Pan, Chao
Lv, Zhicheng
Hua, Xia
Li, Hongyan
The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title_full The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title_fullStr The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title_full_unstemmed The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title_short The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment †
title_sort algorithm and structure for digital normalized cross-correlation by using first-order moment †
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7085734/
https://www.ncbi.nlm.nih.gov/pubmed/32121475
http://dx.doi.org/10.3390/s20051353
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