Total Fractional-Order Variation-Based Constraint Image Deblurring Problem

When deblurring an image, ensuring that the restored intensities are strictly non-negative is crucial. However, current numerical techniques often fail to consistently produce favorable results, leading negative contribute significant dark regions in images. To address this, our study proposes a mathematical model for non-blind image based on total fractional-order variational principles. Our proposed not only guarantees positive intensity values but also imposes limits within specified range. By removing or constraining them prescribed range, we can significantly enhance quality of deblurred The key concept this paper involves converting constrained variational-based problem into unconstrained one through introduction augmented Lagrangian method. facilitate conversion and improve convergence, describe new algorithms introduce novel circulant preconditioned matrix. This matrix effectively overcomes slow convergence typically encountered when using conjugate gradient method framework. approach validated computational tests, demonstrating its effectiveness viability practical applications.