Non-Stationary Hyperspectral Forward Model and High-Resolution

We present in this work a forward model for an Integral Field Unit (IFU) instrument. Our model is general but primarily developed for the Mid Resolution Spectrometer of the Mid Infrared Instrument on board the James Webb Space Telescope (JWST). It takes a 3D spatio-spectral object as input and produces a set of 2D projected data with multiple detectors of different characteristics. However, these 2D outputs suffer from non-stationary spatial and spectral blurring, as well as under-sampling. Our first contribution is the development of the forward model in order to simulate data and the second is the use of this model to reconstruct a full 3D hyperspectral image from the projected measurements. This problem is ill-posed and we propose an algorithm based on the regularized leastsquare approach with convex edge-preserving regularization. We show on the simulation that our proposed model and algorithm allow a better reconstruction than the state of the art algorithm, thanks to spatial and spectral deconvolutions and denoising.