We propose a method, by absorption [1,2,3,4], of determination of the X-ray spectrum emitted by a flash X-ray radiography generator. This approach leads to an ill posed inverse problem very sensitive to the measures precision.
We improve the robustness of the method by introduction of a smoothness constraint on the X-ray spectrum to reconstruct. We also propose an automatic choice of the weight between the measurement and the constraint by using a cross-validation technique.
We present an application on an unusual flash X-ray radiography generator - i.e. 75 ns of duration pulse, 6.5 MeV of maximum energy, 350 Rad for dose - for which an instrument of direct measure has not yet been found.