線性逆問(wèn)題求解的多尺度降階模型
Reduced Order Model for Solving Linear Inverse Problem
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摘要: 基于相對(duì)誤差協(xié)方差矩陣信息，該文給出線性逆問(wèn)題求解的多尺度降階模型，把高階模型的求解問(wèn)題轉(zhuǎn)化為一個(gè)近似的低階模型再進(jìn)行求解．利用該降階模型可以得到與完全模型相當(dāng)?shù)墓烙?jì)效果，同時(shí)又能大大降低逆算法的計(jì)算量，從而有效地解決逆問(wèn)題求解中計(jì)算復(fù)雜度過(guò)高的難題，增強(qiáng)逆問(wèn)題求解算法的可實(shí)施性，采用降階模型進(jìn)行求解還可以增加那些提供顯著信息的點(diǎn)的估計(jì)精度。
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關(guān)鍵詞:
- 降階模型; 逆問(wèn)題; 多尺度逆算法; 相對(duì)誤差協(xié)方差矩陣
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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