Point-of-Care Ultrasound (PoCUS) devices have the potential to enable safe, fast and cost-efficient medical imaging, which can democratize access to medical diagnostics. However, achieving high image quality and real-time performance despite the significant resource constraints of mobile devices is essential for clinical adoption. Fourier-Based Imaging (FBI) is emerging as an alternative to the simple and well established delay-and-sum (DAS) beamforming, as it promises improved image quality albeit higher computational effort. This work investigates an efficient implementation of FBI and evaluates the performance on a Qualcomm Snapdragon 8 system-on-chip (SoC) CPU and GPU using a synthetic radiofrequency (RF) ultrasound dataset. CPU profiling identified the real-to-complex (r2c) Fast Fourier Transform (FFT) as a primary bottleneck, with optimizations reducing runtime from 2993 ms to 892 ms per frame. GPU acceleration via the clFFT library and a custom OpenCL kernel for k-space processing, enhanced through kernel fusion, constant memory usage, and instruction-level tuning, further reduced runtime to 388 ms, a 2.86x speed-up over the optimized CPU version. Although 30 fps real-time performance was not reached under these imaging parameters (2.58 fps), reducing the number of transmitters increased throughput to approximately 6 fps at the expense of image fidelity. These results demonstrate the mobile GPU’s potential for FBI and suggest that real-time execution on next-generation SoCs is within reach.