Sparsity-based denoising of hyperspectral astrophysical data with colored noise: Application to the MUSE instrument

Abstract

This paper proposes a denoising method for hyperspectral astro-physical data, adapted to the specificities of the MUSE (Multi-Unit Spectroscopic Explorer) instrument, which will provide massive integral field spectroscopic observations of the far universe, characterized by very low signal-to-noise ratio and strongly non identically distributed noise. Data are considered as a collection of spectra. The proposed restoration procedure operates on each spectrum by minimizing a penalized data-fit criterion, which takes into account the noise spectral distribution, with additional constraints expressing prior sparsity information in a union of bases. Spectra are modeled as the sum of line and continuous spectra, which are supposed to be sparse in the canonical and the Discrete Cosine Transform bases, respectively. Dealing with colored noise requires specific methodological approaches regarding not only the estimator definition itself, but also hyperparameter tuning and optimization issues. These three points are successively investigated. Promising denoising results are obtained on realistic simulations of astrophysical observations.