The THz frequency spectrum provides an opportunity to explore high-resolution synthetic-aperture-radar (SAR) short-range imaging that can be used for various applications. However, the performance of THz SAR imaging is sensitive to phase errors that can be caused by an insufficient amount of data samples for image formation and by path deviations that can be practically caused by SAR platform vibrations, changes in speed, changes in direction, and acceleration. To solve the former problem, an improved interpolation procedure for backprojection algorithms has been proposed. However, to make these algorithms efficient in handling the latter problem, an additional autofocusing is necessary. In this paper, we introduce an autofocusing procedure based on compressed sensing that is incorporated into the backprojection algorithm. The reconstruction is based on the following calculated parameters: windowed interpolation sinc kernel, and range distances between SAR platform and image pixels in a defined image plane. The proposed approach is tested on real data, which was acquired by the 2\pi FMCW SAR system through outdoor SAR imaging. © 2023 IEEE.