  Using a novel representation for the Martin's real-part formula without the
full scaling property, an almost model-independent description of the
proton-proton differential cross section data at high energies (19.4 GeV - 62.5
GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted
inelastic overlap function presents a peripheral effect (tail) above 2 fm and
the extracted opacity function is characterized by a zero (change of sign) in
the momentum transfer space, confirming results from previous model-independent
analyses. Analytical parametrization for these empirical results are introduced
and discussed. The importance of investigations on the inverse problems in
high-energy elastic hadron scattering is stressed and the relevance of the
proposed representation is commented. A short critical review on the use of
Martin's formula is also presented.
