Circuits, Systems, and Signal Processing

, Volume 38, Issue 5, pp 2072–2096 | Cite as

Mathematical mixed-integer programming for solving a new optimization model of selective image restoration: modelling and resolution by CHN and GA

  • Nour-eddine JoudarEmail author
  • Mohamed Ettaouil


In grey-level image restoration, a prior knowledge of degraded areas allows, thanks to the selective filtering, to achieve a good protection of the image features. In this paper, we propose a quadratic programming-based technique that deals with the issue of details preservation during the restoration process. Based on the classical model of image restoration, we build a modified model by introducing a set of binary variables that indicate the pixel categories. We combine each pixel with the median of its neighbours in a decision rule so that one of them generates the optimal solution. The obtained model is a nonlinear mixed-integer problem where resolution by exact methods is not feasible. In this regard, we use both of the continuous Hopfield neural network and the genetic algorithm to solve the suggested model. Performance of our method is demonstrated numerically and visually by several computational tests.


Image restoration Optimization Selective image restoration Median Continuous Hopfield neural network Penalty function Quadratic programming Genetic algorithm 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and TechnologyUniversity Sidi Mohamed Ben Abdellah FezFezMorocco

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