  We propose a novel theoretical framework to calculate the non-perturbative
QCD quantities. It starts from the dispersion relation of quantum field theory,
separating the high-energy and low-energy scales and using the known
perturbative theories to solve the unknown non-perturbative quantities by the
inverse problem. We prove that the inverse problem of dispersion relation is
ill-posed, with unique but unstable solutions. The regularization methods must
be used to get the stable approximate solutions. The method is based on the
strict mathematics, without any artificial assumptions. We have test some toy
models to vividly show the main features of the inverse problem. It can be
found that this approach can systematically improve the precision of the
solutions.
