期刊文献+

反问题的Landweber迭代法及其应用研究进展 被引量:4

Advances in research in Landweber iterate method for inverse problems and its application
下载PDF
导出
摘要 基于Landweber迭代法在研究反问题中的广泛应用,综述了国内外关于Landweber迭代法用于反问题求解的研究现状、基本理论与相关结论,介绍了Landweber迭代在一些领域,特别是计算机图像重建等方面的应用,并简要提出了关于Landweber迭代法今后的一些研究方向。 This paper introduced studies of domestic and foreign researchers in Landweber iterative method for inverse prob- lems. It overviewed the fundamental theory and conclusion of Landweber iterative method for inverse problems and introduced the application in some areas, especially in image restoration. It put forward briefly some research directions of Landweber iter- ate method in the future.
出处 《计算机应用研究》 CSCD 北大核心 2013年第9期2583-2586,共4页 Application Research of Computers
基金 国家自然科学基金资助项目(NSFC10861001 NSFC11161002)
关键词 反问题 Landweber迭代法 龙格-库塔方法 稳定性 inverse problems Landweber iterative method Runge-Kutta method stability
  • 引文网络
  • 相关文献

参考文献32

  • 1韩波,李莉.非线性不适定问题的求解方法及其应用[M].北京:科学出版社,2011:1-118.
  • 2LANDWEBER L. An iteration formula for fredholm integral equaions of the first kind [ J ]. American Journal Mathematics, 1951,73 (3) :615-624.
  • 3TAUTENHAHN U. On the asymptotieal regularization method for non- linear ill-posed problems [ J ]. Inverse Problems, 1994, 10 ( 6 ) : 1405-1418.
  • 4HANKE M, NEUBAUER A,SCHERZER O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems [ J ]. Nume- rische Mathematik,1995,72( 1 ) :21-37.
  • 5SCHERZER O. Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems [ J]. Journal of Mathematical Analysis and Applications, 1995,194 (3) :911- 933.
  • 6HETTLICH F. The Landweber iteration applied to inverse conductive scattering problems[J]. Inverse Problems,1998,14(4) :931-947.
  • 7NEUBAUER A. On Landweber iteration for nonlinear ill-posed prob- lems in Hilbert scales[ J ]. Numedsche Mathematik,2000,85 (2) : 309- 328.
  • 8JIN Qi-nian,AMATO U. A discrete scheme of landweber iteration for solving nonlinear Ill-posed problems [ J ]. Journal of Mathematical Anatysis and Applications ,2001,253 ( 1 ) : 187-203.
  • 9SCHERZER O. A modified Landweber iteration for solving parameter estimation problems [ J ]. Applied Mathematics Optimization, 1998, 38(1) :45-68.
  • 10KLIGLER P. A derivative free Landweber method for parameter identi-fication in elliptic partial differential equations with application to the manufacture of ear windshields [ D ]. Linz : Johannes Kepler Universi- ty, 2003.

二级参考文献59

共引文献39

同被引文献31

  • 1邵阳,王清华.平滑Chahine迭代算法在光散射法粒度分布反演中的应用[J].南京晓庄学院学报,2008,24(6):15-18. 被引量:2
  • 2王建刚,王福豹,段渭军.加权最小二乘估计在无线传感器网络定位中的应用[J].计算机应用研究,2006,23(9):41-43. 被引量:50
  • 3Griffiths H. Magnetic induction tomography [J]. Measurement Science and Technology, 2001, 12(8): 1126 -1131.
  • 4Mamatjan Y. Imaging of hemorrhagic stroke in magnetic induction tomography: An in vitro study [J]. International Journal of Imaging Systems and Technology, 2014, 24 (2) : 161 -166.
  • 5Merwa R, Hollaus K, Brunner P, et al. Solution of the inverse problem of magnetic induction tomography (MIT) [J] . Physiological Measurement, 2005, 26(2): 241 -249.
  • 6Teniou S, Meribout M, AI-Wahedi K, et al. A Near-infraredbased magnetic induction tomography solution to improve the image reconstruction accuracy in opaque environments [J] . IEEE Transactions on Magnetics, 2013, 49(4) :1361 -1366.
  • 7Jin B, Khan T, Maass P. A reconstruction algorithm for electrical impedance tomography based on sparsely regularization [J]. International Journal for Numerical Methods in Engineering, 2012, 89 (3) : 337 - 353.
  • 8Hsin YW, Soleimani M. Hardware and software design for a National Instrument-based magnetic induction tomography system for prospective biomedical applications [J]. Physiol Measurement,2012,33(5) :863 -879.
  • 9Bras NB, Martins RC, Serra AC, et al. A fast forward problem solver for the reconstruction of biological maps in magnetic induction tomography [J]. IEEE Transactions on Magnetics, 2010, 46( 5) : 1193 -1202.
  • 10Zhang M, Ma L, Soleimani M. Magnetic induction tomography guided electrical capacitance tomography imaging with grounded conductors[J]. Measurement, 2014, 53(7): 171 -181.

引证文献4

二级引证文献16

;
使用帮助 返回顶部