This paper describes the use of microwaves to accurately image objects behind dielectric walls. The data are first simulated by using a finite-difference time-domain code. A large model of a room with walls and objects inside is used as a test case. Since the model and associated volume are big compared to wavelengths, the code is run on a parallel supercomputer. A fixed 2-D receiver array captures all the return data simultaneously. A time-domain backprojection algorithm with a correction for the time delay and refraction caused by the front wall then reconstructs high-fidelity 3-D images. A rigorous refraction correction using Snell's law and a simpler but faster linear correction are compared in both 2-D and 3-D. It is shown that imaging in 3-D and viewing an image in the plane parallel to the receiver array is necessary to identify objects by shape. It is also shown that a simple linear correction for the wall is sufficient.