## 1 Introduction
Therefore, the precise delineation of material property interfaces is one of the most critical requirements in current practice. Total variation (TV) regularization employs the L1 norm for the first-order derivatives of the model parameters' distribution function [36]. The most commonly used TV method is that with the modified stable functional, which solves the problem of non-differentiability at the zero point in traditional TV by introducing a smaller value [37]. This type of regularization can help to obtain high-contrast media or blocky geological structures and has been widely used in geophysical FWI. In addition, the focusing regularization method based on the minimum support (MS) stable functional [38] and its derivatives--the minimum gradient support (MGS) [39] and the minimum support gradient (MSG) [40] stable functionals--further enhance sharp-boundary imaging in geophysical inversions [34; 41], where the MSG method has strong stability and is less dependent on focusing parameter selection. Compared to smooth regularization, TV and focusing methods yield sharper boundaries by constraining the distributions of the model parameter or its gradient changes [30; 41]. This provides a feasible solution for the 3D imaging of high-contrast subsurface anomalies in GPR data. Inversion methods with dual parameters for GPR data typically assume uniform parameter sensitivity, despite fundamental differences between permittivity and conductivity. In practice, the inversion results of permittivity models often yield clear images, while conductivity models' high sensitivity often presents volumetric effects and blurred boundaries in the reconstruction results [11; 14; 28]. To address this, we consider applying different regularizations to constrain the permittivity and conductivity models. Firstly, for permittivity, artifact removal is the main contradiction, as the reconstructed model is sufficiently focused, and any focusing functional may lead to excessive focusing in the imaging results and the waste of computational resources. Secondly, for conductivity, reducing the volume effect--especially obtaining more focused imaging results for sharp anomalous bodies--is of the utmost importance. Thirdly, the superiority of TV regularization in artifact removal and MSG regularization in focusing anomalies, as well as the compatibility of the functional expressions, makes it suitable for the composite model constraint strategy. In this paper, we propose a composite regularization strategy for 3D imaging problems, applying TV regularization to permittivity (optimized for artifact removal without overfocusing) and MSG regularization to conductivity (reducing volumetric effects while enhancing boundary definition) in the GPR FWI framework. We derive the 3D FWI objective function and gradient calculation process with the composite model constraint strategy for multi-offset GPR data. We compare and discuss the inversion results with the TV, MSG, and TV+MSG regularized strategies, as well as the influence of selection factors in model-constrained inversion. The numerical experiments show that the proposed algorithm improves the accuracy and stability of dual-parameter GPR inversion in high-contrast subsurface environments.