在反演过程中利用不同范数准则压制噪声对反演结果的影响

本文对误差数据在各种范数准则下的反演结果进行了详细的分析，在此基础上提出了在反演过程中利用不同范数准则压制噪声的方法，即在反演过程中先用一种范数准则建立目标泛函并求取梯度、再利用另一种范数准则计算修正步长，并在建立目标泛函和求取梯度时引入了非整数次范数准则.该方法有效地避免了在压制噪声过程中的人为干扰，提高了数据的使用率.从合成数据的反演结果可以看出，该方法对噪声具有很好的压制能力.

Using different kinds of norms to suppress the effect of noise in the course of inversion

Based on the analysis of reconstructed results from noisy data under various norms,we propose a method for suppressing noise by using different norms in reconstruction.The objective functional is defined by one kind of norm,and the gradients of the functional to unknown parameters are derived.Another kind of norm is introduced in the calculation of modification steps of the parameters.A non-integral norm objective functional is also defined in this paper.This method effectively avoids artificial operation in suppressing noise and heightens the utilization rate of the data.Examples of reconstruction from synthetic data show that this method is efficacious for suppressing noise.