Spatio spectral reconstruction from low resolution multispectral data : application to the Mid-Infrared instrument of the James Webb Space Telescope

Abstract : This thesis deals with an inverse problem in astronomy. The objective is to reconstruct a spatio-spectral object, having spatial and spectral distributions, from a set of low-resolution multispectral data taken by the imager MIRI (Mid-InfraRed Instrument), which is on board the next space telescope James Webb Space Telescope (JWST). The observed multispectral data suffers from a spatial blur that varies according to the wavelength due to the spatial convolution with a shift-variant optical response (PSF). In addition the multispectral data also suffers from severe spectral degradations because of the spectral filtering and the integration by the detector over broad bands. The reconstruction of the original object is an ill-posed problem because of the severe lack of spectral information in the multispectral dataset. The difficulty then arises in choosing a representation of the object that allows the reconstruction of this spectral information. A common model used so far considers a spectral shift-invariant PSF per band, which neglects the spectral variation of the PSF. This simplistic model is only suitable for instruments with a narrow spectral band, which is not the case for the imager of MIRI. Our approach consists of developing an inverse problem framework that is summarized in four steps: (1) designing an instrument model that reproduces the observed multispectral data, (2) proposing an adapted model to represent the sought object, (3) exploiting all multispectral dataset jointly, and finally (4) developing a reconstruction method based on regularization methods by enforcing prior information to the solution. The overall reconstruction results obtained on simulated data of the JWST/MIRI imager show a significant increase of spatial and spectral resolutions of the reconstructed object compared to conventional methods. The reconstructed object shows a clear denoising and deconvolution of the multispectral data. We obtained a relative error below 5% at 30 dB, and an execution time of 1 second for the l₂-norm algorithm and 20 seconds (with 50 iterations) for the l₂/l₁-norm algorithm. This is 10 times faster than the iterative solution computed by conjugate gradients.
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Mohamed Elamine Hadj-Youcef. Spatio spectral reconstruction from low resolution multispectral data : application to the Mid-Infrared instrument of the James Webb Space Telescope. Signal and Image processing. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLS326⟩. ⟨tel-02170514⟩

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