B樣條函數(shù)在二維導(dǎo)體橫截面輪廓成象中的應(yīng)用
APPLICATION OF B-SPLINE IN RECONSTRUCTION OF 2-D CONDUCTOR CROSS-SECTION
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摘要: 本文將B樣條函數(shù)應(yīng)用于根據(jù)多入射方向下的后散射場對二維導(dǎo)體柱橫截面形狀的反演,并將整個(gè)反演過程轉(zhuǎn)化為兩次非線性優(yōu)化過程。由于兩次優(yōu)化的目標(biāo)函數(shù)的導(dǎo)數(shù)都是可求得的,因此采用基于梯度的優(yōu)化算法,如Broyden-Fletcher-Goldfard-Shanno變尺度算法(簡稱BFGS方法)。第一次優(yōu)化最佳的等效圓柱的半徑和深度,然后在第二次優(yōu)化過程中再進(jìn)一步優(yōu)化導(dǎo)體柱橫截面的控制節(jié)點(diǎn)以得到反演的形狀。最后,以數(shù)值結(jié)果驗(yàn)證了該方法的有效性,并討論了該方法的抗噪聲性能。
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關(guān)鍵詞:
- B樣條函數(shù); Frechet微分; BFGS方法; 輪廓成象
Abstract: B-spline is applied to the reconstruction of 2-D conductor cross-section via backscat-tered field in near region illuminated by plane waves with different incident directions. The whole inverse problem may be viewed as a two-stage optimal procedure, and the optimal algorithm based on gradient, such as BFGS algorithm, is adopted as the gradient of the objective functions which may be derived by using Frechet differential. In the first step, the position and the radius of optimal circular cylinder are obtained, then in the second step, with above results as its initial values, the shape of 2-D cylinder can be reconstructed. The robustness of the proposed method is tested using different numerical results, and the effects of noise are discussed. -
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