In this paper we present a local interpolation-based variant of the well-known polar format algorithm used for synthetic aperture radar (SAR) image formation. We develop the algorithm to match the capabilities of the application-specific logic-in-memory processing paradigm, which off-loads lightweight computation directly into the SRAM and DRAM. Our proposed algorithm performs filtering, an image perspective transformation, and a local 2D interpolation, and supports partial and low-resolution reconstruction. We implement our customized SAR grid interpolation logic-in-memory hardware in advanced 14 nm silicon technology. Our high-level design tools allow to instantiate various optimized design choices to fit image processing and hardware needs of application designers. Our simulation results show that the logic-in-memory approach has the potential to enable substantial improvements in energy efficiency without sacrificing image quality.