The generalized cross validation method for the selection of regularization parameter in geophysical diffraction tomography
نویسندگان
چکیده
Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. The method that we choose is the regularization by derivative matrices. There is a crucial problem in regularization, which is the selection of the regularization parameter λ. In this work we use generalized cross validation (GCV) as a tool for the selection of λ. GCV was presented by Golub et al. (1979), and it is used in this work in geophysical diffraction tomography, where the objective is to obtain the 2–D velocity distribution from the measured values of the scattered acoustic field. The results are compared to those obtained using L-curve, and also Θcurve, which is an extension of L-curve (Santos and Bassrei, 2007). We present several simulation results with synthetic data, and in general, the results using GCV are better that the other two approaches.
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