We present an inverse problem approach to jointly solve a problem of deconvolution and demixing of sources from 4D (x, y, λ, t) astronomical data obtained by observing a super- nova and its host galaxy at different epochs. In order to obtain supernova spectra of high photometric quality, we take special care of avoiding demixing biases and deconvolution artifacts caused by the very limited size of the field of view. We assert the performances of our method on realistic simulated data.