With the capability of shearing resistance, Fourier digital holography will be of great significance once applied to terahertz imaging field. In this paper, the 2.52 THz Fourier digital holography is simulated based on the parameters of surface array detector. Then the reconstructed image can be obtained for a certain object using Fourier holography. By adding Gaussian noise and salt pepper noise to the object, the influences of noise on the object are studied with the mean and median filters. The experimental results reveal that, the reconstructed image can be distinguished though affected by noise, when the variance of Gaussian noise is below 0.20, and image contours become distinct after filtering; when the variance of Gaussian noise is above 0.20, the reconstructed image cannot be distinguished even filtered. When the density of salt and pepper noise reaches up to 0.20, the reconstructed image submerges, but it can be observed again by mean filtering or median filtering. Therein the mean filtering is superior to median filtering.