Abstract: The Fourier Transform Pairs (FTP) between the image domain and its corresponding range-compressed phase history domain is critical for autofocus. Different from the frequency-domain algorithms, this requirement of FTP is both complicated and difficult to be met in the time-domain algorithms. For a swift and effective reconstruction and autofocus processing of imagery created by the time-domain algorithm, the necessary improvement and optimization in the Fast Factorized Back-Projection (FFBP) is performed, presenting an Improved FFBP (IFFBP) algorithm further. Through the pseudo-polar coordinate system, the IFFBP is able to pave the way for autofocus application. Also, in view of the practical requirements for data processing, the IFFBP uses a moderate-accuracy Inertial Measurement Unit (IMU) to achieve a coarse compensation，and combines with the Phase Gradient Autofocus (PGA) to make a fine compensation. Finally, the simulation results and the collected data sets verify and validate the proposed approach.