Fourier single pixel imaging utilizes pre-programmed patterns for laser spatial distribution modulation to reconstruct intensity image of the target through reconstruction algorithms. The approach features non-locality and high anti-interference performance. However, Poor image quality is induced when the target of interest is occluded in Fourier single pixel imaging. To address the problem, a deep learning-based image inpainting algorithm is employed within Fourier single pixel imaging to reconstruct partially obscured targets with high quality. It applies a distance-based segmentation method to segment obscured regions and the target of interest. Additionally, it utilizes an image inpainting network that combines multi-scale sparse convolution and transformer architecture, along with a reconstruction network that integrates Channel Attention Mechanism and Attention Gate modules to reconstruct complete and clear intensity images of the target of interest. The proposed method significantly expands the application scenarios and improves the imaging quality of Fourier single pixel imaging. Simulation and real-world experimental results demonstrate that the proposed method exhibits the high inpainting and reconstruction capacity in the conditions of hard occlusion and down-sampling.