In this work, a novel hybrid algorithm is introduced that combines the range migration algorithm (RMA) and the back projection algorithm (BPA). The traditional image reconstruction algorithms used for synthetic aperture radar each have trade-offs between computational efficiency and imaging accuracy. The proposed hybrid RMA–BPA approach leverages the computational efficiency of RMA for the initial image reconstruction and object detection, followed by BPA for the refined, high resolution of the cropped region of data. The method of focusing computational resources on the smaller cropped datasets that contain the objects significantly reduces the processing time compared to that of traditional standalone BPA. The hybrid approach’s performance was evaluated over three different scenarios, providing a reduction in computation time for each scenario. Due to the algorithm’s approach to crop the dataset for the specific object, the increased efficiency varied. The different scenarios each produced different times to compute; however, the most impressive result delivered a 75.2% reduction in computation time compared to traditional BPA, without sacrificing the accuracy of the image. The hybrid approach is especially suited for applications that require precise object detection in healthcare, oil and gas, security, and industrial inspections.