反褶积信号恢复

本文根据地震勘探中的反褶积问题,提出了反褶积信号恢复问题,首先讨论了无噪情形下的反褶积信号恢复问题,引入τ-P变换后,讨论了有噪情形下的反褶积信号恢复问题。本文将提出的反褶积信号恢复问题转化为从多个高次多项式中提取最佳近似公因式的问题.一方面,给出了在最大近似公因式阶次已知时最大近似公因式的求解方法;另一方面给出了在阶次未知时获得最大近似公因式的最优阶次的算法。并通过实例证明本文所提出的问题、相应的理论结果及算法是正确的。

In the paper, the problem of Deconvolutional Signal Recovery is presented based on the deconvolution problem in seismic prospecting. First , the problem of Deconvolutional Signal Recovery is discussed without noise , then the problem of Deconvolutional Signal Recovery is discussed with noise with the help of Tau-P transform.Here , the problem of Deconvolutional Signal Recovery is converted into the problem to obtain the optimal approximate common factor from many polynomials with high degree. On one hand , the method to obtain the optimal approximate common factor is presented when its degree is given . On the other hand , the algorithm to obtain the optimal approximate common factor is given when its de- gree is unknown. Finally the example demonstrates that the problem presented in this paper , corresponding theory and algorithm are correct.