Low-dose radiographic inspection is a growing trend in industry to minimize radiation risks to humans and the environment. However, reduction in radiation dose often introduces significant noise, which affects image quality and hinders accurate identification of subtle defects. This study addresses this issue by introducing a novel phenomenon called aperiodic reverse stochastic resonance (ARSR), observed in nonlinear systems excited by aperiodic binary signals. ARSR enables simultaneous amplitude amplification and reversal of signals under specific noise conditions. Leveraging ARSR, we propose an image denoising framework for low-dose radiographic inspections. First, a set of projection data is obtained by using Radon transform to reduce the dimensionality of X-ray images from different angles. Then, the projection data is modulated based on the ARSR system. Finally, the image is reconstructed based on the inverse Radon transform. Simulations and experimental comparison results in welding applications validate the effectiveness of the framework, demonstrating significant improvements in image quality for low-dose radiographic defect detection. Unlike advanced methods such as Gaussian filtering, BM3D, and DnCNN, which operate at the pixel level, ARSR performs denoising at the projection data stage, reducing noise impact, preserving original information, and focusing on physical data processing during imaging. This approach enhances the detection of subtle defects, highlighting the potential of stochastic resonance in image processing.