remote sensing of colors

from an unknown family (Ui) 0<i<(n+1) , Ui are in Rm (m is 1,2 or 3 typically)

I get the n*n(+1)/2 terms (Vj) where
Vj is one of the (Ui+Uk)/2

The question is : if the (Vj) are given, how can I find (Ui)?

we lack this solution to analyse color distribution in remote sensing.
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