<title>Regularization method preserving photometry for Richardson-Lucy restoration</title>

Abstract

The success of Richardson-Lucy (RL) algorithm is that it forces the restored image to be non-negative and to conserve global flux at each iteration. The problem with RL algorithm is that it produces solutions that are highly unstable, with high peaks and deep valleys. Our aim is to modify RL algorithm in order do regularize it while preserving positivity and total photometry as far as possible. Data instances that are not compatible with others can cause singularities in the restoration solution. So, we have an ill-posed problem and a regularization method is needed to replace it to a well-posed problem. The regularization approach overcomes this difficulty by choosing among the possible objects one 'smooth' that approximate the data. The basic underlying idea in most regularization approaches is the incorporation of 'a priori' knowledge into the restoration. In this article we try to give a simple method of spatial regularization deriving from RL algorithm in order to overcome the problem of noise amplification during the image reconstruction process. It is very important in astronomy and remote sensing to regularize images while having under control their photometric behavior. We propose a new reconstruction method preserving both the global photometry and local photometric aspects.