We develop a new inversion method that may be advantageously applied to remote sounding in atmospheric physics. The technique is based on the synthesis of the inversion operator which can be used in noisy measurements where the success of classical regularization and optimal estimation methods strongly depends on the accurate knowledge of the a priori atmospheric state. We outline the benefits of the method: robustness, full control of validity range as well as easy assessment of the smoothing error. An example of spectral inversion is extensively analyzed in the context of aerosol retrievals from limb occultation experiments.