Gaussian Mixture Model-Hierarchical Domain Constraint Framework Enhanced VBIM for Solving the Inverse Scattering Problems

• Published in: IEEE transactions on geoscience and remote sensing Vol. 62; pp. 1 - 14
• Main Authors: Zhou, Hongguang, Zhao, Yanwen, Wang, Yan, Han, Danfeng, Ji, Lin, Hu, Jun, Nie, Zaiping
• Format: Journal Article
• Language: English
• Published: New York IEEE 2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Cells; Cluster analysis; Constraint modelling; Gaussian mixture model (GMM); Hypothesis testing; Ill posed problems; Inverse problems; Inverse scattering; Iterative methods; Lower bounds; Permittivity; Probabilistic models; Pseudorandom; Quadratic programming; quadratic programming (QP); Receivers; Regularization; Testing; Upper bound; Upper bounds; variational Born iterative method (VBIM)
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2024.3370184

Based on the assumption that the pseudorandom characteristic of variational Born iterative method (VBIM), the retrieved contrast parameter distribution in the discrete cells complies with the Gaussian mixture model (GMM). This article presents a constrained optimization framework that combines GMM and a hierarchical domain constraint (HDC) strategy for solving inverse scattering problems (ISPs). This GMM-HDC framework divides the whole inversion process into several stages, each stage operating within a reduced domain and subject to lower bound and upper bound (UB) constraints. The reduced inversion domain is determined by the GMM's cluster analysis, thereby eliminating the need for manual threshold selection. And the HDC strategy offers a re-classification mechanism to avoid misclassification of scatterer cells. By narrowing the inversion domain, this approach effectively reduces the solution's dimensionality, and mitigating the ill-posedness of ISPs. The bound constraint is determined by a hypothesis testing method. When there is prior information of contrast bound, the solution during iteration may not be within the exact bound due to the ill-posedness of ISPs. Therefore, the flexibility-bound constraint can provide more stability. When the prior information is not available, the determined UB is also guaranteed to converge probabilistically to the exact UB in case of degradation. In each iteration, a quadratic programming (QP) formula is introduced to solve the inverse subproblem in the VBIM, which enables the incorporation of the contrast range determined by the GMM-HDC framework. The formula includes both Tikhonov (TK) and total variation (TV) regularization terms. Several typical models, including synthetic and experimental measurement data, are presented to verify the performance of the proposed method.