An automatic selection method for EIT regularization parameters based on maximum marginal likelihood estimation

As a non-invasive imaging modality, Electrical Impedance Tomography (EIT) derives its value from the ability to estimate internal conductivity distributions based on measurements taken at the boundary. A central challenge in EIT image reconstruction stems from its ill-posed nature, necessitating the application of regularization. Conventionally, the selection of regularization parameters involves manual and often tedious tuning, a step that critically determines the fidelity of the reconstructed images. This paper introduces a novel, fully automated approach for regularization parameter estimation based on maximum marginal likelihood estimation, enabling unsupervised parameter determination directly from observational data without manual intervention or ground truth references. Our method establishes a statistically principled framework that optimally balances data fidelity and prior constraints, yielding high-quality reconstructed images with clear boundaries and minimal artifacts. Extensive numerical experiments across diverse two and three dimensional EIT scenarios demonstrate the method's robustness, adaptability, and superior performance compared to conventional approaches. The proposed technique not only eliminates the subjectivity inherent in manual parameter selection but also provides a rigorous probabilistic foundation for EIT reconstruction, offering a significant advancement in the field of medical and industrial imaging.