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	A general axiomatic system for image resolution quantification
	Jiang, M ; Wang, G ; Ma, XM
	2006
关键词	imaging system point spread function (PSF) image resolution arithmetic mean geometric mean POINT SPREAD FUNCTION SPIRAL CT IMAGES COMPUTED-TOMOGRAPHY RESTORATION NOISE
英文摘要	In this paper, we generalize our previously published axiom system for quantification of image resolution and prove that any resolution measure consistent with the new axiom system must be a homogeneous symmetric function of order 1/2 of the eigenvalues of the covariance matrix of the PSF. We demonstrate that the previous axiom system is not consistent with the affine transformation axiom. We propose a weak combination axiom to replace the previous strong combination axiom and use it to solve this conflict. It is remarkable that the original finding in one-dimension by Wang and Li can be easily rediscovered with aid of the weak combination axiom, instead of using the previous strong combination axiom. If the previous axiom system is modified with the weak combination axiom and augmented with the affine transformation axiom, the resolution measure is shown to be proportional to the squared root of the geometric mean of the eigenvalues of the covariance matrix of the PSF. Relevant discussions and possible extensions are also provided. (c) 2005 Elsevier Inc. All rights reserved.; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; 2; 462-473; 315
语种	英语
出处	SCI
出版者	数学分析与应用杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157899]
专题	数学科学学院 环境科学与工程学院
推荐引用方式 GB/T 7714	Jiang, M,Wang, G,Ma, XM. A general axiomatic system for image resolution quantification. 2006-01-01.

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