A comparative study of game theory techniques for blind deconvolution

The aim of this study is to lay emphasis on the potential of the use of Game theory to deal with Blind image Deconvolution.  We consider a static game of two players.  Player one controls the image intensity while the player two controls the blur kernel.  In this game each player aims at minimizing his own functional.  The outcome of the game is a pair of strategies: a deblurred image and an estimation of the blur kernel, that minimizes two functionals.  We determine the optimal image deblurring using two particular game theoretic approaches, recently introduced: the Nash method [Meskine D., Moussaid N., Berhich S. Blind image deblurring by game theory. Proceedings of the 2nd International Conference on Networking, Information Systems & Security (NISS '19). 31 (2019)] and the Kalai–Smorodinsky solution method [Nasr N., Moussaid N., Gouasnouane O. The Kalai Smorodinsky solution for blind deconvolution. Computational and Applied Mathematics. 41, 222 (2022)].  We evaluate the performance of two techniques through numerical experiments and using some objective quality metrics.

deblurring
game theory
Multi-objective optimization
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