Conformable fractional order variation-based image deblurring

Image deblurring (ID) plays a vital role in various applications, including photography, medical imaging, and surveillance. Traditional ID methods often face challenges in preserving fine details and handling complex blurring scenarios due to expensive calculations. In this paper, a novel approach utilizing conformable fractional derivative (CFD) to address these challenges and improve the effectiveness of ID is presented. CFD offer a flexible framework for capturing and exploiting the non-local and non-linear properties inherent in images. Additionally, we propose a new circulant preconditioned matrix that ensures a fast convergence rate. The proven analytical property of the new preconditioner ensures fast convergence rates. The efficiency and efficacy of our algorithm is demonstrated by numerical experiments.