A stopping criterion to halt iterations at the Richardson-Lucy deconvolution of radiographic images

Abstract

Radiographic images, as any experimentally acquired ones, are affected by spoiling agents which degrade their final quality. The degradation caused by agents of systematic character, can be reduced by some kind of treatment such as an iterative deconvolution. This approach requires two parameters, namely the system resolution and the best number of iterations in order to achieve the best final image. This work proposes a novel procedure to estimate the best number of iterations, which replaces the cumbersome visual inspection by a comparison of numbers. These numbers are deduced from the image histograms, taking into account the global difference G between them for two subsequent iterations. The developed algorithm, including a Richardson-Lucy deconvolution procedure has been embodied into a Fortran program capable to plot the 1st derivative of G as the processing progresses and to stop it automatically when this derivative - within the data dispersion - reaches zero. The radiograph of a specially chosen object acquired with thermal neutrons from the Argonauta research reactor at Institutode Engenharia Nuclear - CNEN, Rio de Janeiro, Brazil, have undergone this treatment with fair results.