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超声逆散射图象重建问题中截断奇异值分解正则化方法研究

DOI: 10.11834/jig.2003010408

Keywords: 计算机图象处理(520?6040),超声,逆散射,图象重建,奇异值分解,正则化

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Abstract:

为解决超声逆散射成像问题中的非线性性,人们需要反复地求解前向散射方程和逆散射方程,以达到对全场和未知函数的精确近似,从而根据这一未知函数的精确近似,较好地重建物体内部的断层图象.前向散射方程是一个适定的方程组,可以采用通常的方法进行求解;而逆散射方程则是一个不适定性的方程组,即使数据中存在一个微小的误差,都可能引起解的较大偏离,因此,对这个不适定方程组的求解问题是整个迭代算法成功的关键.而在不适定性问题的求解过程中,正则化参数的选取又是非常重要的.求解不适定性方程的传统方法是Tikhonov正则化方法,这一方法的实质是在传统最小二乘方法上加上一个小于1的滤波因子,对于超声逆散射成像问题来说,效果并不太好.本文将截断奇异值分解正则化方法应用于逆散射方程的求解问题中,并对正则化参数的选取方法进行修正.数值仿真结果表明,这一方法配合适当的正则化参数选取,可以更好地滤除噪声,提高重建图象的质量与可信度,同时还可以减小迭代过程中的计算量.

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