The quality control of composite multilayered materials and structures using nondestructive tests is of high interest for numerous applications in the aerospace and aeronautics industry. One of the established nondestructive methods uses microwaves to reveal defects inside a three-dimensional (3-D) object. Recently, there has been a tendency to extrapolate this method to higher frequencies (going to the subterahertz spectrum) which could lead to higher resolutions in the obtained 3-D images. Working at higher frequencies reveals challenges to deal with the increased data rate and to efficiently and effectively process and evaluate the obtained 3-D imagery for defect detection and recognition. To deal with these two challenges, we combine compressive sensing (for data rate reduction) with a dedicated image processing methodology for a fast, accurate, and robust quality evaluation of the object under test. We describe in detail the used methodology and evaluate the obtained results using subterahertz data acquired of two calibration samples with a frequency modulated continuous wave system. The applicability of compressive sensing within this context is discussed as well as the quality of the image processing methodology dealing with the reconstructed images.