Data inversion for over-resolved spectral imaging in astronomy

TL;DR

This paper introduces a novel physically-based inversion method for 3D spectral imaging in astronomy, achieving 1.5 times higher resolution than traditional techniques by modeling the data formation process and using a semi-parametric approach.

Contribution

The work presents a new inversion technique that models the data acquisition process in continuous variables and employs a semi-parametric Gaussian decomposition for super-resolution in spectral imaging.

Findings

Achieves 1.5-fold resolution improvement over conventional methods

Demonstrates effectiveness on real and simulated astronomical data

Provides a physically-based, deterministic regularization framework

Abstract

We present an original method for reconstructing a three-dimensional 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 two-dimensional sensor. The originality of this work lies in the physical modelling, in integral form, of this process of data formation in continuous variables. The inversion is lso 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.