Sparsity-based spatial-spectral restoration of muse astrophysical hyperspectral data cubes

We consider the restoration of extragalactic deep field hyperspectral imaging data, in the context of the forthcoming MUSE instrument. Joint spatial-spectral restoration is addressed by taking into account the three-dimensional point spread function (PSF) of the instrument and the noise statistical distribution, with strong spectral variations for both of them. Since objects of interest have limited spatial extensions, restoration is formulated for sub-cubes with restricted spatial coverage. Prior information is incorporated by means of sparsity constraints in the spectral domain, using a specific dictionary with physically meaningful elementary features. We decompose the too high-dimensional underlying optimization problem into two steps by exploiting the separability property of the PSF. First, spectra are processed independently, where sparsity performs spectral dimension reduction. Then, a computationally tractable three-dimensional restoration problem is solved. Simulations reveal the interest of this approach, where restoration efficiently performs the separation of two close objects and the unmixing of their spectra.