Data Inversion for Over-Resolved Spectral Imaging in Astronomy

• Published in: IEEE journal of selected topics in signal processing 2008-10, Vol.2 (5), p.802-811
• Main Authors: Rodet, T., Orieux, F., Giovannelli, J.-F., Abergel, A.
• Format: Article
• Language: English
• Subjects: Apertures; Applications; Astronomy; Astrophysics; Bayesian estimation; Computer Science; Diffraction gratings; Engineering Sciences; Format; Image Processing; Image reconstruction; Imaging; Infrared spectra; Instrumentation and Methods for Astrophysic; interpolation; inverse problems; Inversions; irregular sampling; IRS Spitzer; Mathematical models; Mathematics; Optical diffraction; Optical distortion; Optical imaging; Optical sensors; over-resolved imaging; Physics; Sciences of the Universe; Signal and Image processing; Slits; Space telescopes; Spectra; spectral imaging; Spectrographs; Statistics; Statistics Theory; Studies; Telescopes
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2008.2006392

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.