Volume 6, Issue 1
Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 262-275.

Published online: 2013-06

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• Abstract

Image deconvolution problems with a symmetric point-spread function arise in many areas of science and engineering. These problems often are solved by the Richardson-Lucy method, a nonlinear iterative method. We first show a convergence result for the Richardson-Lucy method. The proof sheds light on why the method may converge slowly. Subsequently, we describe an iterative active set method that imposes the same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the Richardson-Lucy method and typically require less computational effort.

65R20, 65R32, 65K05

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@Article{NMTMA-6-262, author = {}, title = {Iterative Methods of Richardson-Lucy-Type for Image Deblurring}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {1}, pages = {262--275}, abstract = {

Image deconvolution problems with a symmetric point-spread function arise in many areas of science and engineering. These problems often are solved by the Richardson-Lucy method, a nonlinear iterative method. We first show a convergence result for the Richardson-Lucy method. The proof sheds light on why the method may converge slowly. Subsequently, we describe an iterative active set method that imposes the same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the Richardson-Lucy method and typically require less computational effort.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.mssvm14}, url = {http://global-sci.org/intro/article_detail/nmtma/5903.html} }
TY - JOUR T1 - Iterative Methods of Richardson-Lucy-Type for Image Deblurring JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 262 EP - 275 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.mssvm14 UR - https://global-sci.org/intro/article_detail/nmtma/5903.html KW - Constrained ill-posed problem, nonnegativity, active set method, image restoration AB -

Image deconvolution problems with a symmetric point-spread function arise in many areas of science and engineering. These problems often are solved by the Richardson-Lucy method, a nonlinear iterative method. We first show a convergence result for the Richardson-Lucy method. The proof sheds light on why the method may converge slowly. Subsequently, we describe an iterative active set method that imposes the same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the Richardson-Lucy method and typically require less computational effort.

M. K. Khan, S. Morigi, L. Reichel & F. Sgallari. (2020). Iterative Methods of Richardson-Lucy-Type for Image Deblurring. Numerical Mathematics: Theory, Methods and Applications. 6 (1). 262-275. doi:10.4208/nmtma.2013.mssvm14
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