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線性逆問題求解的多尺度降階模型

文成林,  周福娜,  楊國勝

文成林, 周福娜, 楊國勝. 線性逆問題求解的多尺度降階模型[J]. 電子與信息學報, 2004, 26(12): 1888-1894.
引用本文: 文成林, 周福娜, 楊國勝. 線性逆問題求解的多尺度降階模型[J]. 電子與信息學報, 2004, 26(12): 1888-1894.
Wen Cheng-lin, Zhou Fu-na, Yang Guo-sheng. Reduced Order Model for Solving Linear Inverse Problem[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1888-1894.
Citation: Wen Cheng-lin, Zhou Fu-na, Yang Guo-sheng. Reduced Order Model for Solving Linear Inverse Problem[J]. Journal of Electronics & Information Technology, 2004, 26(12): 1888-1894.

線性逆問題求解的多尺度降階模型

Reduced Order Model for Solving Linear Inverse Problem

  • 摘要: 基于相對誤差協(xié)方差矩陣信息，該文給出線性逆問題求解的多尺度降階模型，把高階模型的求解問題轉化為一個近似的低階模型再進行求解．利用該降階模型可以得到與完全模型相當?shù)墓烙嬓Ч瑫r又能大大降低逆算法的計算量，從而有效地解決逆問題求解中計算復雜度過高的難題，增強逆問題求解算法的可實施性，采用降階模型進行求解還可以增加那些提供顯著信息的點的估計精度。
    Abstract: Based on relative error covariarice matrix (RECM) information, a reduced-order model is proposed for solving linear inverse problem. The reduced-order model turns the high order model into an approximate lower order model, which can efficiently alleviate the computational load of the inversion algorithm. Thus, the computational complexity difficulty arose in the solution of linear inverse problem can be conquered, and this in turn promotes the implementation of the inversion algorithm. In addition, the reduced-order model can improve the estimate precision of those points that provide significant information to the reconstruction of the object.
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  • Miller E L, Willsky A S. A multiscale approach to sensor fusion and the solution of linear inverse problems[J].Applied and computational Harmonic analysis.1995, 2(6):127-147[2]Throne R D, Olson L G. A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography[J].IEEE Trans. on Bio. Engineering.2002, 49(9):1054-1059[3]Peter J, Jaszczak R J, Hutton B F, Hudson H M. Fully adaptive temporal regression smoothing in gated cardiac SPECT[J]. IEEE Trans. on Nuclear Science, 2001, NS-48(1): 16-23.[4]Oraintara S, Karl W C, Castanon D A, Nguyen T Q. A method for choosing the regularization parameter in generalized Tikhonov regularized linear inverse problems[J], Image Processing, 2000,7(1): 93-96.[5] Wen Chenglin, Zhang Yanfeng. The multi-scale distributed hierarchical fusion algorithm for the solution of linear inverse problem. .[J].ICMLC.2003, Xian:-[6]堯德中,周映春,范思陸,陳霖,敖新宇.多維延時相關MUSIC方法-一種求解腦電逆問題的新方法.電子學報,2001,29(4):522-525.[7]周福娜.多傳感器數(shù)據(jù)融合與線性逆問題的多尺度求解:[碩士論文],開封:河南大學,2004.[8]文成林,周東華,多尺度估計理論及應用[M].北京:清華大學出版社,2002:第二章.
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出版歷程
  • 收稿日期:  2003-09-22
  • 修回日期:  2004-05-08
  • 刊出日期:  2004-12-19

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