A Three-Dimensional Model-Based Inversion Algorithm Using Radial Basis Functions for Microwave Data

We present a three-dimensional (3D) model-based inversion algorithm for inverting electromagnetic data. In our approach, the models are described by points in the 3D space and the so-called radial basis functions are used as the interpolation functions for connecting these points. The use of the radial basis functions renders the surface of the target intrinsically smooth. The L
₂
-norm and weighted L
₂
-norm regularization schemes are employed to constrain the curvature and to further smooth the surface of the target. We tested this inversion algorithm using both synthetic and experimental data sets. The inversion results demonstrate that both the shapes and material properties of the target are well reconstructed. As a complementary algorithm to the pixel-based (tomographic) inversion algorithms, the model-based inversion algorithm has fewer parameters to invert; hence, it has a higher computational efficiency. The model-based inversion algorithm also gives the users the freedom to construct an initial model based on their knowledge and other related information. It helps to reduce the non-uniqueness in the data interpretation.