In order to realize rapid imaging of Fourier telescopy, an approach of image reconstruction via sparse sampling is proposed and the accurate image reconstruction by using sparse Fourier samples is investigated.Firstly, based on compressed sensing theory and the sparsity or compressiveness of object images in transformation domains, the optimization model of image reconstruction via sparse sampling is established.Then, appropriate masks for random and sparse sampling are constructed to sample Fourier components of object images.Finally, object images are reconstructed accurately through nonlinear optimization by using the random and sparse samples.Experimental results indicate that the RMS errors of reconstructed images between 20%~30% sampling and full sampling are only 4%~6%, which shows that the proposed approach can realize accurate image reconstruction by using random and sparse Fourier samples and can reduce the amount of measurement samples greatly.The method lowers the requirements of costs and complexity to Fourier telescopy systems for rapid imaging effectively.