Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed ...Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform（FFT）algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision.展开更多
In this paper we propose a mixed regularization method for ill-posed prob-lems.This method combines iterative regularization methods and continuous regular-ization methods effectively.First it applies iterative regula...In this paper we propose a mixed regularization method for ill-posed prob-lems.This method combines iterative regularization methods and continuous regular-ization methods effectively.First it applies iterative regularization methods in which there is no continuous regularization parameter to solve the normal equation of the ill-posed problem.Then continuous regularization methods are applied to solve its residual problem.The presented mixed regularization algorithm is a general framework.Any iterative regularization method and continuous regularization method can be combined together to construct a mixed regularization method.Our theoretical analysis shows that the new mixed regularization method is with optimal order of error estimation and can reach the optimal order under a much wider range of the regularization parameter than the continuous regularization method such as Tikhobov regularization.Moreover,the new mixed regularization method can reduce the sensitivity of the regularization parameter and improve the solution of continuous regularization methods or iterative regularization methods.This advantage is helpful when the optimal regularization pa-rameter is hard to choose.The numerical computations illustrate the effectiveness of our new mixed regularization method.展开更多
基金supported by the National Natural Science Foundation of China(41304022,41174026,41104047)the National 973 Foundation(61322201,2013CB733303)+1 种基金the Key laboratory Foundation of Geo-space Environment and Geodesy of the Ministry of Education(13-01-08)the Youth Innovation Foundation of High Resolution Earth Observation(GFZX04060103-5-12)
文摘Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform（FFT）algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision.
基金This research is supported by the National Natural Science Foundation of China under the grant number 11471328.
文摘In this paper we propose a mixed regularization method for ill-posed prob-lems.This method combines iterative regularization methods and continuous regular-ization methods effectively.First it applies iterative regularization methods in which there is no continuous regularization parameter to solve the normal equation of the ill-posed problem.Then continuous regularization methods are applied to solve its residual problem.The presented mixed regularization algorithm is a general framework.Any iterative regularization method and continuous regularization method can be combined together to construct a mixed regularization method.Our theoretical analysis shows that the new mixed regularization method is with optimal order of error estimation and can reach the optimal order under a much wider range of the regularization parameter than the continuous regularization method such as Tikhobov regularization.Moreover,the new mixed regularization method can reduce the sensitivity of the regularization parameter and improve the solution of continuous regularization methods or iterative regularization methods.This advantage is helpful when the optimal regularization pa-rameter is hard to choose.The numerical computations illustrate the effectiveness of our new mixed regularization method.
