Integration of CNNs and Spline Expansion for Subsurface Profiling of Arbitrary Shape Objects

This paper introduces a novel approach to challenging subsurface profiling problems through the utilization of neural networks. The proposed method transforms the inverse problem into a regression task, leveraging cubic spline expansion (CSE) to efficiently define the target's geometry with a reduced set of parameters. This reduction not only simplifies the problem's complexity but also effectively preserves the capability to model diverse set of arbitrary curvilinear shapes. By incorporating this modeling approach, the defined problem aims to determine a target vector that includes the permittivity value, CSE controlling points, and the object's center coordinates. The utilization of a streamlined Convolutional Neural Network (CNN) architecture enables learning from measured scattered field amplitudes to predict the related target vector. The obtained results showcase the algorithm's efficacy in reconstructing profiles with various shapes within a relatively broad permittivity range.