With the increasing complexity of public security, indoor security inspection demands higher imaging precision and real-time performance. Traditional X-ray and millimeter-wave imaging systems exhibit limitations in safety, resolution, and anti-interference capability. Near-field synthetic aperture radar, with its high resolution and non-contact advantages, has emerged as a promising alternative. However, although the back projection algorithm achieves precise focusing, speckle noise significantly degrades image quality, limiting its practical application. To address this issue, this paper proposes and implements a fast filtering strategy and hardware-oriented solution for back projection imaging. At the algorithm level, local statistics are rapidly computed using integral images, combined with adaptive γ modeling to achieve efficient speckle suppression while preserving edge details. At the hardware level, image blocking, multi-unit parallel reuse, and pipelined architecture are employed to accelerate filtering and reduce latency, while neighborhood extension is used to mitigate edge distortion caused by blocking. Experimental results demonstrate that, for a 300×300 synthetic aperture data, the filtering time is reduced to approximately 6.67 ms, equivalent number of looks increases from 5.19 to 11.47, edge structure deviation decreases from 0.19 to 0.13, and peak signal-to-noise ratio reaches 39.27 dB, significantly outperforming traditional Lee or Kuan filters. Hardware implementation results indicate that the proposed architecture achieves advantages in resource utilization and real-time performance, confirming its practicality in efficient and scalable indoor synthetic aperture radar image filtering and providing reliable technical support for next-generation indoor security inspection systems.