  We present in detail the basic ingredients contained in bi-local holography,
representing a constructive scheme for reconstructing AdS bulk theories in
Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is
seen to be given by a double Fourier transform. All order interactions are
explicitly specified through the collective action. This generates bulk Feynman
(Witten) diagrams (at tree and loop level). We give details of the four-point
case evaluation. It is noted that the bi-local construction goes beyond the
assumptions in various discussions of non-locality.
