Terahertz three-dimensional (3D) imaging is an important research direction for terahertz (THz) imaging technology, because 3D images of a sample can provide richer distribution information than 2D images. The main algorithm-control parameters that affect the accuracy of compressed 3D reconstructions are the number of iteration and the sparse restriction parameter. In this paper, we use subjective and objective evaluations to analyze the influences of these parameters on the reconstruction results for an ideal situation. Considering that noise is generated because the actual target plate is inhomogeneous, we mainly study the influences of the control parameters in reconstruction algorithms containing different levels of Gaussian noise on reconstructed results. The results show that when the number of iteration is 200, sparse restriction parameter is 0.02, 0.1 and 0.1 for the ideal case and Gaussian noise variance of 0.0005 and 0.001, respectively.