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	Relaxation strategy for the Landweber method
	Han, Guanghui ; Qu, Gangrong ; Jiang, Ming
	2016
关键词	Landweber iteration Relaxation strategy Image reconstruction Weighted least-squares ITERATIVE METHODS LINEAR-EQUATIONS RECONSTRUCTION ALGORITHMS IMAGE-RECONSTRUCTION FEASIBILITY PROBLEM CONVERGENCE SYSTEMS ACCELERATION PROJECTIONS SIRT
英文摘要	The Landweber iteration is a general method for the solution of linear systems which is widely applied for image reconstructions. The convergence behavior of the Landweber iteration is of both theoretical and practical importance. By the representation of the iterative formula and the convergence results of the Landweber iteration, we derive the optimal relaxation method under the minimization of the spectral radius of the newly derived iterative matrix. We also establish the iterative relaxation strategy to accelerate the convergence for the Landweber iteration when only the biggest singular value is available. As an immediate result, we derive the corresponding results for Richardson's iteration for the symmetric nonnegative definite linear systems. Finally, numerical simulations are conducted to validate the theoretical results. The advantage of the proposed relaxation strategies is demonstrated by comparing with the existing strategies. (C) 2016 Elsevier B.V. All rights reserved.; National Basic Research Program of China (973 Program) [2015CB-351803]; National Science Foundation of China [61421062, 61520106004]; Sino-German Center [GZ 1025]; National Natural Science Foundations of China [61271012, 61071144]; SCI(E); EI; ARTICLE; grqu@bjtu.edu.cn; ming-jiang@ieee.org; 87-96; 125
语种	英语
出处	SCI ; EI
出版者	SIGNAL PROCESSING
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/437057]
专题	数学科学学院
推荐引用方式 GB/T 7714	Han, Guanghui,Qu, Gangrong,Jiang, Ming. Relaxation strategy for the Landweber method. 2016-01-01.

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