Weakly Constrained Lucy–Richardson with Applications to Inversion of Light Scattering Data

Lucy-Richardson (LR) is a classical iterative regularization method largely used for the restoration of nonnegative solutions. LR finds applications in many physical problems, such as for the inversion of light scattering data. In these problems, there is often additional information on the true solution that is usually ignored by many restoration methods because the related measurable quantities are likely to be affected by non-negligible noise. In this article we propose a novel Weakly Constrained Lucy-Richardson (WCLR) method which adds a weak constraint to the classical LR by introducing a penalization term, whose strength can be varied over a very large range. The WCLR method is simple and robust as the standard LR, but offers the great advantage of widely stretching the domain range over which the solution can be reliably recovered. Some selected numerical examples prove the performances of the proposed algorithm.