We introduce a new inverse population synthesis algorithm (DINBAS3D) which aims to recover the star formation and metallicity histories from galactic spectra. We investigate the use of a dynamical basis of three simple stellar population spectra that is specific for each galaxy. Our goal is to recover a robust star formation history that minimizes degeneracy effects which are very common in high resolution histories methods. In this work, we detail the method and present our findings when we apply DINBAS3D to synthetic spectra with known parameters, we compare our results with similar methods and find good agreement between them.