正则化超声Lanczos反卷积的NCB成像分析

The Imaging Analysis for Normalization Supersonic Lanczos Deconvolution by NCB Algorithm

摘要:

Lanczos方法是求解大尺度逆问题的一种有效方法, 这种方法的特点是可以把大尺度问题转化为小尺度问题, 而且可以把解严格限制在Krylov子空间, 只是它存在的半收敛性问题需要进一步克服。为了确保算法的有效性、稳定性和精确性, Lanczos混合法(Lanczos-hybrid)试图通过正则参数的适当选取来解决这个问题。文章在Hansen提出的正则化参数选取的NCP方法基础上, 设计了一种新的算法NCB, 即利用Burg功率谱代替NCP中的经典周期图谱, 较好地克服了Lanczos 的半收敛性问题, 降低了解对迭代次数的敏感性, 得到了大尺度反卷积病态问题的稳定解; 并以超声RF信号为例进行仿真, 结果表明, NCB的成像效果比GCV要好。

Abstract:

The Lanczos method, which can restrict the solution to Krylov subspace precisely, is an effective method to solve the large-scale inverse problem, but the problem of semi-convergence needs to be overcome. To ensure the validity, the stability and the precision of the solution, Lanczos-hybrid can be used to solve this semi-convergence problem through the right selection of a regularization parameters. Based on NCP (The Normalized Cumulative Periodogram normalization accumulation frequency spectrum ) method proposed by Hansen in 2006 for the selection of a regularization parameters, designed is a new algorithm NCB, in which the Burg power spectrum replaces classical periodogram. With the new method, the semi-convergence problem existing in the Lanczos method is solved and the sensitivity of the solution to the number of iterations is reduced, and the stable solution for the large-scale inverse problem is obtained. Taking the ultrasonic RF signal as an example, the imaging effect for a variable method was analyzed, and the results show that the NCB is better than GCV.