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	Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms
	Qu, Gangrong ; Wang, Caifang ; Jiang, Ming
	2009
关键词	Image reconstruction singular value decomposition (SVD) the Landweber scheme weighted least-squares ITERATIVE ALGORITHMS FEASIBILITY PROBLEM LINEAR-EQUATIONS TECHNIQUE SART TOMOGRAPHY REGULARIZATION PROJECTION SYSTEMS
英文摘要	The Landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases. The convergence of the Landweber scheme is of both theoretical and practical importance. Using the singular value decomposition (SVD). we derive all iterative representation formula for the Landweber scheme and consequently establish the necessary and sufficient conditions for its convergence. In addition to verifying the necessity and sufficiency of known convergent conditions, we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results. Moreover, it is found that the Landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values. Furthermore, the limits of the Landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.; Computer Science, Artificial Intelligence; Engineering, Electrical & Electronic; SCI(E); EI; 7; LETTER; 2; 435-440; 18
语种	英语
出处	EI ; SCI
出版者	ieee transactions on image processing
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/246551]
专题	数学科学学院
推荐引用方式 GB/T 7714	Qu, Gangrong,Wang, Caifang,Jiang, Ming. Necessary and Sufficient Convergence Conditions for Algebraic Image Reconstruction Algorithms. 2009-01-01.

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