Astronomical image denoising using dictionary learning^⋆

¹ Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, SAp/SEDI, Service d’Astrophysique, CEA Saclay, 91191 Gif-sur-yvette Cedex, France
e-mail: simon@beckouche.fr
² GREYC CNRS-ENSICAEN-Université de Caen, 6 Bd du Maréchal Juin, 14050 Caen Cedex, France

Received: 16 November 2012
Accepted: 27 January 2013

Abstract

Astronomical images suffer a constant presence of multiple defects that are consequences of the atmospheric conditions and of the intrinsic properties of the acquisition equipment. One of the most frequent defects in astronomical imaging is the presence of additive noise which makes a denoising step mandatory before processing data. During the last decade, a particular modeling scheme, based on sparse representations, has drawn the attention of an ever growing community of researchers. Sparse representations offer a promising framework to many image and signal processing tasks, especially denoising and restoration applications. At first, the harmonics, wavelets and similar bases, and overcomplete representations have been considered as candidate domains to seek the sparsest representation. A new generation of algorithms, based on data-driven dictionaries, evolved rapidly and compete now with the off-the-shelf fixed dictionaries. Although designing a dictionary relies on guessing the representative elementary forms and functions, the framework of dictionary learning offers the possibility of constructing the dictionary using the data themselves, which provides us with a more flexible setup to sparse modeling and allows us to build more sophisticated dictionaries. In this paper, we introduce the centered dictionary learning (CDL) method and we study its performance for astronomical image denoising. We show how CDL outperforms wavelet or classic dictionary learning denoising techniques on astronomical images, and we give a comparison of the effects of these different algorithms on the photometry of the denoised images.