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Iterative Methods of Richardson-Lucy-Type for Image Deblurring

Published online by Cambridge University Press:  28 May 2015

M. K. Khan ,
S. Morigi ,
L. Reichel  and
F. Sgallari
M. K. Khan*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
S. Morigi*
Affiliation:
Department of Mathematics, University of Bologna, P.zza Porta San Donato 5, Bologna, Italy
L. Reichel*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
F. Sgallari*
Affiliation:
Department of Mathematics-CIRAM, University of Bologna, Via Saragozza 8, Bologna, Italy
*
Corresponding author.Email address:kazim@math.kent.edu
Corresponding author.Email address:serena.morigi@unibo.it
Corresponding author.Email address:reichel@math.kent.edu
Corresponding author.Email address:fiorella.sgallari@unibo.it
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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.

Keywords

65R2065R3265K05Constrained ill-posed problemnonnegativityactive set methodimage restoration
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 1 , February 2013 , pp. 262 - 275
Copyright
Copyright © Global Science Press Limited 2013

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