Geodesic
Semi-convergence and relaxation parameters for a class of SIRT algorithms
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 321-336
This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography (image reconstruction from projections).
Classification : 65F10, 65R32
Keywords: SIRT methods, cimmino and DROP iteration, semi-convergence, relaxation parameters, tomographic imaging 
@article{ETNA_2010__37__a5,
     author = {Elfving,  Tommy and Nikazad,  Touraj and Hansen,  Per Christian},
     title = {Semi-convergence and relaxation parameters for a class of {SIRT} algorithms},
     journal = {Electronic transactions on numerical analysis},
     pages = {321--336},
     year = {2010},
     volume = {37},
     zbl = {1205.65148},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a5/}
}
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%A Nikazad,  Touraj
%A Hansen,  Per Christian
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%J Electronic transactions on numerical analysis
%D 2010
%P 321-336
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%G en
%F ETNA_2010__37__a5
Elfving,  Tommy; Nikazad,  Touraj; Hansen,  Per Christian. Semi-convergence and relaxation parameters for a class of SIRT algorithms. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 321-336. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a5/