Blind image deblurring using fractional order derivatives and total variation: A Nash equilibrium approach

Fractional-order modeling represents a viable approach for addressing the inherent limitations of total variation in image deblurring tasks.  This technique is achieved through the discretization of fractional derivatives and has demonstrated significant advancements in enhancing the quality of reconstructed images.  Building upon the success of our previous work on blind deconvolution, where we utilized an image-based total variation to reduce the staircase effect, we analyze and test a novel blind deblurring model based on $\beta$-order fractional derivatives using the Nash game.  This game employs the same type of players, each with their strategy to find an optimal solution, as defined in our previous work.  Furthermore, we compare our proposed method with classical and fractional-order methods with different $\beta$ parameters.  Our numerical results demonstrate, that our method achieves higher effectiveness and better image quality compared to existing reconstruction methods.