  Astronomical images suffer a constant presence of multiple defects that are
consequences of the intrinsic properties of the acquisition equipments, and
atmospheric conditions. 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. While designing a dictionary beforehand leans
on a guess of the most appropriate representative elementary forms and
functions, the dictionary learning framework offers to construct the dictionary
upon the data themselves, which provides us with a more flexible setup to
sparse modeling and allows to build more sophisticated dictionaries. In this
paper, we introduce the Centered Dictionary Learning (CDL) method and we study
its performances 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 effect of these different algorithms on
the photometry of the denoised images.
