The Planetary Fourier Spectrometer (PFS) onboard Mars Express (MEx) is the instrument with the highest spectral resolution observing Mars from orbit since January 2004. It permits studying the atmospheric structure, major and minor compounds. The present time version of the calibration is limited by the effects of mechanical vibration, currently not corrected. We proposed here a new approach to correct for the vibrations based on semi-blind deconvolution of the measurements. This new approach shows that a correction can be done efficiently with 85% reduction of the artifacts, in a equivalent manner to the stacking of 10 spectra. Our strategy is not fully automatic due to the dependence on some regularisation parameters. It may be applied on the complete PFS dataset, correcting the large-scale perturbation due to microvibrations for each spectrum independently. This approach is validated on actual PFS data of Short Wavelength Channel (SWC), perturbed by microvibrations. A coherence check can be performed and also validate our approach. Unfortunately, the coherence check can be done only on the first 310 orbits of MEx only, until the laser line has been switch off. More generally, this work may apply to numerically "deshake" Fourier Transform Spectrometer (FTS), widely used in space experiments or in the laboratory.