We propose a novel tomographic method, nonlinear Gaussian process tomography (nonlinear GPT), that uses the Laplace approximation to impose constraints on non-negative physical quantities, such as the emissivity in plasma optical diagnostics. While positive-valued posteriors have previously been introduced through sampling-based approaches in the original GPT method, our alternative approach implements a logarithmic Gaussian process (log-GP) for faster computation and more natural enforcement of non-negativity. The effectiveness of the proposed log-GP tomography is demonstrated through a case study using the Ring Trap 1 (RT-1) device, where log-GPT outperforms existing methods, standard GPT, and the Minimum Fisher Information (MFI) methods in terms of reconstruction accuracy. The results highlight the effectiveness of nonlinear GPT for imposing physical constraints in applications to an inverse problem.

翻译：我们提出了一种新颖的层析成像方法——非线性高斯过程层析成像（nonlinear GPT），该方法利用拉普拉斯近似对非负物理量（如等离子体光学诊断中的辐射率）施加约束。虽然在原始GPT方法中，已通过基于采样的方法引入了正值后验分布，但我们的替代方法实现了一种对数高斯过程（log-GP），以实现更快的计算和更自然地强制执行非负性。通过对环阱1号（RT-1）装置的案例研究，证明了所提出的log-GP层析成像的有效性，其中log-GPT在重建精度方面优于现有方法、标准GPT以及最小费舍尔信息（MFI）方法。这些结果突显了非线性GPT在反问题应用中施加物理约束的有效性。