Synthetic aperture (SA) ultrasound imaging is a well-known technique in which RF signals for every transmit and receive element combinations is first obtained and a 2-way-focused image is synthetically formed afterwards. Despite its benefits, one of its main shortcomings is reduced penetration depth caused by low acoustic power from single element firing. To address this challenge, we propose a spatial prediction filtering technique called the frequency-space (F-X) prediction filtering (FXPF), which adaptively constructs a spatial filter that rejects random noise and off-axis clutter components directly from the time-aligned channel data. By utilizing the information in the spatial domain, FXPF enhances the signal-to-noise ratio (SNR) by suppressing random noise within the transducer bandwidth, which typically cannot be filtered by temporal bandpass filters.