Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates

In log-polar coordinates, the conventional data sampling method is to sample uniformly in the log-polar radius and polar angle directions, which makes the sample at the fovea of the data denser than that of the peripheral. The central oversampling phenomenon of the conventional sampling method gives...

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Autores principales:	Chan Li, Dayong Lu, Hao Dong
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	quantum computation quantum data representations data scaling up biarcuate interpolation log-polar coordinates Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/3c122bdce38e4d449388fe06db01dafa
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spelling	oai:doaj.org-article:3c122bdce38e4d449388fe06db01dafa2021-11-25T17:29:51ZQuantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates10.3390/e231114621099-4300https://doaj.org/article/3c122bdce38e4d449388fe06db01dafa2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1462https://doaj.org/toc/1099-4300In log-polar coordinates, the conventional data sampling method is to sample uniformly in the log-polar radius and polar angle directions, which makes the sample at the fovea of the data denser than that of the peripheral. The central oversampling phenomenon of the conventional sampling method gives no more efficient information and results in computational waste. Fortunately, the adaptive sampling method is a powerful tool to solve this problem in practice, so the paper introduces it to quantum data processing. In the paper, the quantum representation model of adaptive sampled data is proposed first, in which the upper limit of the sampling number of the polar angles is related to the log-polar radius. Owing to this characteristic, its preparation process has become relatively complicated. Then, in order to demonstrate the practicality of the model given in the paper, the scaling up algorithm with an integer scaling ratio based on biarcuate interpolation and its circuit implementation of quantum adaptive sampled data is given. However, due to the special properties of the adaptive sampling method in log-polar coordinates, the interpolation process of adaptive sampled data becomes quite complicated as well. At the end of this paper, the feasibility of the algorithm is verified by a numerical example.Chan LiDayong LuHao DongMDPI AGarticlequantum computationquantum data representationsdata scaling upbiarcuate interpolationlog-polar coordinatesScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1462, p 1462 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	quantum computation quantum data representations data scaling up biarcuate interpolation log-polar coordinates Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	quantum computation quantum data representations data scaling up biarcuate interpolation log-polar coordinates Science Q Astrophysics QB460-466 Physics QC1-999 Chan Li Dayong Lu Hao Dong Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
description	In log-polar coordinates, the conventional data sampling method is to sample uniformly in the log-polar radius and polar angle directions, which makes the sample at the fovea of the data denser than that of the peripheral. The central oversampling phenomenon of the conventional sampling method gives no more efficient information and results in computational waste. Fortunately, the adaptive sampling method is a powerful tool to solve this problem in practice, so the paper introduces it to quantum data processing. In the paper, the quantum representation model of adaptive sampled data is proposed first, in which the upper limit of the sampling number of the polar angles is related to the log-polar radius. Owing to this characteristic, its preparation process has become relatively complicated. Then, in order to demonstrate the practicality of the model given in the paper, the scaling up algorithm with an integer scaling ratio based on biarcuate interpolation and its circuit implementation of quantum adaptive sampled data is given. However, due to the special properties of the adaptive sampling method in log-polar coordinates, the interpolation process of adaptive sampled data becomes quite complicated as well. At the end of this paper, the feasibility of the algorithm is verified by a numerical example.
format	article
author	Chan Li Dayong Lu Hao Dong
author_facet	Chan Li Dayong Lu Hao Dong
author_sort	Chan Li
title	Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
title_short	Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
title_full	Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
title_fullStr	Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
title_full_unstemmed	Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates
title_sort	quantum representations and scaling up algorithms of adaptive sampled-data in log-polar coordinates
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3c122bdce38e4d449388fe06db01dafa
work_keys_str_mv	AT chanli quantumrepresentationsandscalingupalgorithmsofadaptivesampleddatainlogpolarcoordinates AT dayonglu quantumrepresentationsandscalingupalgorithmsofadaptivesampleddatainlogpolarcoordinates AT haodong quantumrepresentationsandscalingupalgorithmsofadaptivesampleddatainlogpolarcoordinates
_version_	1718412278406053888

Quantum Representations and Scaling Up Algorithms of Adaptive Sampled-Data in Log-Polar Coordinates

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