We present an original method for reconstruction of hyperspectral objects (two spatial and one spectral dimensions) from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. The originality of the work lies in the fact that both measurement model and inversion method are tackled in continuous (spatial and spectral) variables. The method is built in a deterministic regularization framework and enable to achieve both deconvolution and over-resolution. Results show that the method is able to evidence spatial structures not detectable by means of conventional methods. The spatial resolution is shown to be improved by a factor 1.5. We discuss our data processing approach for the new generation of infrared to millimeter space observatories launched in 2009 (Herschel and Planck).