Scale invariant divergences for signal and image reconstruction

The subject of this paper is the reconstruction of a signal or an image under constraints of non negativity and of constant sum. The sum constraint is imposed by the use of scale invariant divergences, which allows the development of simple iterative reconstruction algorithms. Two families of divergences between two data fields p and q are considered, the a-divergence and the β-divergence. A procedure is applied to make them scale-invariant w.r.t. p and q. The resulting method is an interior point type algorithm useful in the context of ill-posed problems. Numerical illustrations are given for the deconvolution of a solar spectrum and an interferometric image.