The importance of mobile high-performance computing has emerged in numerous battlespace applications at the tactical edge in hostile environments. Energy efficient computing power is a key enabler for diverse areas ranging from real-time big data analytics and atmospheric science to network science. However, the design of tactical mobile data centers is dominated by power, thermal, and physical constraints. Presently, it is very unlikely to achieve required computing processing power by aggregating emerging heterogeneous many-core processing platforms consisting of CPU, Field Programmable Gate Arrays and Graphic Processor cores constrained by power and performance. To address these challenges, we performed a Synthetic Aperture Radar case study for Automatic Target Recognition (ATR) using Deep Neural Networks (DNNs). However, these DNN models are typically trained using GPUs with gigabytes of external memories and massively used 32-bit floating point operations. As a result, DNNs do not run efficiently on hardware appropriate for low power or mobile applications. To address this limitation, we proposed for compressing DNN models for ATR suited to deployment on resource constrained hardware. This proposed compression framework utilizes promising DNN compression techniques including pruning and weight quantization while also focusing on processor features common to modern low-power devices. Following this methodology as a guideline produced a DNN for ATR tuned to maximize classification throughput, minimize power consumption, and minimize memory footprint on a low-power device.