The introduction of compressed sensing (CS) effectively pushes the development of single-pixel THz imaging due to reducing the experimental time and avoiding raster scanning. In this work, a CS method based on photoinduced dynamic masks is employed to recover a THz diffraction field in the time domain, and an inverse Fresnel diffraction (IFD) integral is adopted to remove the influence of the diffraction and reconstruct the sharp THz spectral image in a single-pixel THz imaging system. The compatibility of the CS and IFD algorithms are validated on the simulation and experiment. Besides, the reconstruction effects are also systematically analyzed by reducing the measurement number and varying the diffraction distance, respectively. This work supplies a novel thinking for improving the practicability of single-pixel THz imaging.