Nonlinear forward and reconstruction framework for terahertz computed tomography

Terahertz computed tomography (THz-CT) aims to reconstruct the internal structure of objects using non-ionizing THz waves, offering broad potential for industrial non-destructive testing. However, most existing methods adopt the straight-line propagation assumption as in X-ray CT, neglecting the significant refraction of THz waves in inhomogeneous media, which limits reconstruction accuracy. To address this issue, we propose a nonlinear forward modeling and reconstruction framework. Specifically, we develop an iterative ray propagation algorithm based on Snell's law to model nonlinear THz propagation paths involving both unknown refractive indices and interfaces. Based on this nonlinear forward model, we formulate an inverse problem for reconstructing the refractive index. This problem is highly ill-posed, nonconvex, and nonsmooth, making it challenging for gradient-based methods; therefore, we adopt a derivative-free differential evolution algorithm for robust reconstruction. Once the refractive index and interface geometry are recovered, the nonlinear THz path can be accurately computed. We then formulate the transmission coefficient recovery as a total variation (TV)-regularized optimization problem and solve it efficiently using the alternating direction method of multipliers (ADMM). Experimental results on real THz datasets demonstrate that our method significantly outperforms existing linear-ray-based approaches in reconstruction accuracy.