在研究奇异值分解、最小二乘法的基础上,采用空间域方法研究超声逆散射成像问题.通过脉冲基和点匹配的方法将泛函方程转换为代数方程,运用迭代算法解决方程的非线性问题.利用Picard准则判断方程的不适定程度,并采用均值处理和截断奇异值分解正则化2种方法对方程进行求解.实验结果证明,该方法可以较好地滤除噪声,提高重建图像的质量和可信度,减少迭代过程中的计算量.%Ultrasound inverse scattering imaging is studied by a method of spatial domain based on Singular Value Decomposition(SVD) and least squares solution. By converting the functional equation to algebraic equation with the approach of pulse basis and pointed-match, nonlinear problems are solved by iterative algorithm. The extent of ill-posedness can be determined by Picard theory and the equations can be solved by two kinds of methods of average handling and truncated singular value decomposition. Experimental results illustrate that solving ill-posed equations with appropriate regularization parameter can filter out the noise better and improve the quality of the reconstructed image and credibility, and also can reduce the amount of computation in the iterative process.
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