Multi-element synthetic aperture techniques employing subaperture processing over successive firing steps can produce good image quality with simple front-end hardware but are susceptible to motion and phase aberration artifacts. We explore correlation processing using fully common spatial frequencies of overlapping subapertures to adapt beamforming for motion and phase aberrations. Signals derived from the subset of elements representing common spatial frequencies exhibit significantly higher correlation coefficients than those from signals computed using the entire subaperture. In addition, the correlation coefficient decreases linearly with subaperture separation for complete subaperture signals, but remains nearly constant with subaperture separation if only common spatial frequencies are used. Adaptive multi-element synthetic aperture imaging with correlation processing using fully common spatial frequencies is tested on experimental RF data acquired from a diffuse scattering phantom using a 3.5 MHz, 128-element transducer array. The results indicate that common spatial frequencies can be used efficiently for correlation processing to correct motion and phase aberration for adaptive multi-element synthetic aperture imaging.