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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。
The Lanczos method is an efficient method to solve large-scale inverse problems. The method is characterized by the fact that large-scale problems can be transformed into small-scale problems and that the solution can be strictly restricted to the Krylov subspace, but its semi-convergence problem Need to overcome further. In order to ensure the validity, stability and accuracy of the algorithm, Lanczos-hybrid attempts to solve this problem by proper selection of regular parameters. Based on the NCP method proposed by Hansen for the regularization parameter selection, a new algorithm, NCB, is designed. By using the Burg power spectrum instead of the classical periodic pattern in NCP, this paper overcomes the semi-convergence problem of Lanczos and reduces The sensitivities to the number of iterations are known, and the stable solution to large-scale deconvolution pathological problems is obtained. The simulation of the ultrasound RF signal is used as an example. The results show that the imaging effect of NCB is better than that of GCV.