The Kalai Smorodinsky solution for blind deconvolution

This paper addresses the problem of blind deconvolution solved in the game theory framework. The problem is formulated as a two-player static game of complete information. One player is associated with the image intensity, while the other one, is in charge with the point spread function. Hence, our present proposition amounts to searching for a particular game theoretic solution, the Kalai Smorodinsky solution. Celebrated for possessing attractive properties, it ensures equal marginal gains over all objectives. By this setting, the minimizer arises as the selected Kalai Smorodinsky solution of this game. We use the NBI method to generate the pareto front as we determine the Kalai Smorodinsky solution geometrically. Finally, we present some numerical illustrations, well-known objective image quality metrics like “peak signal to noise ratio” (PSNR), “mean square error” (MSE) and the “structural similarity index measure” (SSIM) (Wang et al. in IEEE Trans Image Process 13(4):600–612, 2004, https://doi.org/10.1109/TIP.2003.819861), are used to evaluate the performance of our approach.