Flash radiography enables the diagnosis of rapid physical processes, yet the instantaneous nature of image acquisition results in a severely limited number of projections. This study investigates uncertainty quantification methods for computed tomography (CT) image reconstruction under the typical scenario of a single projection view. Current approaches for single-view CT uncertainty quantification often adopt oversimplified physical models, assuming linearized optical path equations with Gaussian noise. To address this limitation, we derive a more realistic nonlinear reconstruction framework based on the Lambert-Beer’s law, constructing an exponential attenuation model for transmittance with an integrated Gaussian noise term. This formulation yields a nonlinear posterior probability density function, which is subsequently sampled using the Randomize-Then-Optimize (RTO) algorithm combined with Gibbs sampling. The reconstructed image and its associated uncertainty are obtained through statistical analysis of the sampled data. Numerical simulations validate the proposed method, with comparative results against conventional linearized models demonstrating its superior potential for accurate uncertainty estimation in image reconstruction.