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We present an original method for reconstructing a 3-D object having two spatial dimensions and one spectral dimension from data provided by the infrared slit spectrograph on board the Spitzer Space Telescope. During acquisition, the light flux is deformed by a complex process comprising four main elements (the telescope aperture, the slit, the diffraction grating, and optical distortion) before it reaches the 2-D sensor. The originality of this work lies in the physical modeling, in integral form, of this process of data formation in continuous variables. The inversion is also approached with continuous variables in a semi-parametric format decomposing the object into a family of Gaussian functions. The estimate is built in a deterministic regularization framework as the minimizer of a quadratic criterion. These specificities give our method the power to over-resolve. Its performance is illustrated using real and simulated data. We also present a study of the resolution showing a 1.5-fold improvement relative to conventional methods.