The Generalized Cross Validation Method for the Selection of Regularization Parameter in Geophysical Diffraction Tomography

Abstract

Inverse problems are usually ill-posed in such a way that it is necessary to use some method to reduce their deficiencies. For this purpose, we use the regularization by derivative matrices, known as Tikhonov regularization. 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 is used here for an application 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 Θ-curve, which is an extension of L-curve. We present several simulation results with synthetic data, and in general the results using GCV are equal or eventually better than the other two approaches.

Barbieri Criterion for Solution Appraisal in Geophysical Diffraction Tomography

“…The question of the regularization of the inverse problem and the search for the optimal normalization parameter λ was studied by Santos & Bassrei (2007), who used the L curve and the Theta curve to choose λ. More recently, Santos et al (2021) used generalized cross validation for the same purpose.…”