Journal of Scientific Computing

, Volume 74, Issue 2, pp 786–804 | Cite as

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

  • Alessandro Buccini
  • Marco Donatelli
  • Fabio Ferri


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.


Lucy–Richardson algorithm Light scattering Particle sizing 

Mathematics Subject Classification

65R32 78A46 78A10 



The authors would like to thank the reviewers for their insightful comments that greatly improved the readability and the overall quality of this work. The work of the first two authors is supported in part by MIUR - PRIN 2012 N. 2012MTE38N and by a grant of the group GNCS of INdAM. The work of the last author was partially supported by Fondazione Cariplo, Grant n. 2016-0648, Project: Romancing the stone: size controlled HYdroxyaPATItes for sustainable Agriculture (HYPATIA).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesKent State UniversityKentUSA
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità degli Studi dell’InsubriaComoItaly
  3. 3.Dipartimento di Scienza e Alta Tecnologia, To.Sca.LabUniversità degli Studi dell’InsubriaComoItaly

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