北京生物醫(yī)學(xué)工程

離散化誤差對(duì)二維EIT影響的初步定量研究

Preliminary quantitative study on influence of FEM discretization error on EIT forward and inverse problem

作者：吳克堅(jiān) 付峰趙清波劉銳崗陶峰徐清華楊繼慶董秀珍

單位：                      第四軍醫(yī)大學(xué)生物醫(yī)學(xué)工程學(xué)院數(shù)理教研室(西安710032)        

關(guān)鍵詞：電阻抗斷層成像；圖像重建；有限元法；模型誤差

分類號(hào)：

出版年·卷·期（頁(yè)碼）：2013·32·3（221-225）

摘要：

目的結(jié)合具體重建算法，定量討論有限元離散化誤差對(duì)正逆問題的影響。方法利用軟件NETGEN產(chǎn)生7個(gè)不同剖分規(guī)模的圓域模型，以其中最密剖分模型為參考，討論其他模型的邊界電壓誤差，然后提出重建圖像質(zhì)量函數(shù)D、結(jié)構(gòu)相似度SSIM和誤差總和TE三種重建圖像評(píng)價(jià)指標(biāo)，對(duì)無噪聲和含有不同信噪比噪聲兩種情況的NOSER算法重建圖像進(jìn)行了比較。結(jié)果在無噪聲和噪聲信噪比不太小 (>35dB) 的仿真實(shí)驗(yàn)中，剖分愈密成像質(zhì)量愈高。當(dāng)剖分規(guī)模達(dá)到一定程度時(shí)，圖像質(zhì)量提高幅度有限。結(jié)論有限元離散化誤差對(duì)于EIT問題至關(guān)重要，對(duì)于NOSER這種線性近似的非迭代算法，圓域模型選擇中等剖分規(guī)模(如2000～3000個(gè)單元)即可達(dá)到很高的精度。

Objective The influence of FEM discretization error on EIT forward and inverse problem was quantitatively studied with specific algorithms. Methods Circular models of 7 different meshing scales were generated by using NETGEN. The boundary voltage errors of other meshes were studied by using the mesh with the highest resolution as the reference. Three reconstruction evaluation indexes were proposed to compare the NOSER reconstruction images with and without noises of different SNR：reconstruction quality function D，structural similarity image measurement (SSIM) and total error (TE). Results In simulations where there was no noise or noise of SNR bigger than 35dB，the more the number of elements and nodes was，the finer the reconstruction images were. When the meshing scale reached a certain degree，the improvement of the reconstruction was limited. Conclusions The FEM discretization error is crucial to EIT. For non-iterative algorithms with linear approximation such as NOSER，moderate meshing scale (2000-3000 elements) of circular model satisfies the accuracy requirement.

參考文獻(xiàn)：

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