On the Richardson-Lucy Algorithm with A Varying Point Spread Function along The Iterations

Abstract: This work analyses the soundness of two algorithms, Fishsint and Almexp to improve images using the Richardson-Lucy (RL) algorithm under a varying Point Spread Function (PSF) along the iterations. A plethora of methods based on Richardson-Lucy has been published, but no further proposal involving such an alternative has been published. Whereas the unnamed predecessor of Fishsint addressed only small size synthetic images under a blind fashion procedure, Fishsint and Almexp employs an algorithm Wdet to determine the initial PSF and all subsequent values after each iteration, respectively. Fishsint performs a loop, where the last determined PSF improves the previously obtained image and vice versa. Its original unnamed version has been modified in the present work by entering a previously determined initial PSF to accelerate the convergence. The algorithm Almexp, as well, uses the algorithm Wdet to determine the PSF of the last obtained image to deconvolve itself. Therefore, whereas the Fishsint unnamed predecessor used an initial guess PSF - chosen by the customer - Almexp determines the PSF always through the algorithm Wdet. Fishsint and Almexp furnish final images which outperform those obtained with the original Richardson-Lucy approach working under a constant PSF along the iterations. Hence, in order to carry out a comparison between their performances, all the algorithms have been embedded into an ad hoc written Fortran 90 program. The results corroborate the soundness of a varying PSF along the iterations with the Richardson Lucy algorithm. Keywords: Richardson-Lucy, varying PSF along iterations, image improvement, neutron radiograph