Towards a Nash game strategy approach to blind image deconvolution: a fractional-order derivative variational framework

Abstract

Image restoration is a critical process aimed at recovering degraded images, often impacted by factors including motion blur, sensor blurring, defocused photography, optical aberrations, atmospheric distortions, and noise-induced blur. The inherent challenge lies in the typical scenario where both the original image and the blur kernel (Point Spread Function, PSF) are unknown. This restorative process finds applications in various fields, including sensing, medical imaging, astronomy, remote sensing, and criminal investigations. This paper introduces an innovative approach to blind image deconvolution based on Nash game theory. Our focus is placed on restoring linearly corrupted images without processing explicit knowledge of the original image or the blur kernel (PSF). The proposed method formulates blind deconvolution as a two-player static game, with one player dedicated to image deblurring and the other focused on estimating the PSF. The optimal solution is characterized as Nash equilibrium, resulting in effective image restoration. Moreover, we present an enhanced game formulation that incorporates fractional-order derivatives. This unique extension has the potential to improve image restoration accuracy and resilience, leading to breakthroughs in blind image deconvolution and practical applications.