Blind and Non-blind Image Deconvolution Involving a Total Fractional-order Variation Model
摘要
Blind image deconvolution constitutes an inverse problem with the objective of recovering a sharp image from its associated degraded observation, characterized by blurriness and/or noise. This task is particularly complicated due to the absence of knowledge about the blur-kernel, or point spread function (PSF). The ill-posed nature of this problem stems from the existence of an endless number of image-blur combinations which may feasibly generate the degraded image. Consequently, the use of regularization techniques becomes imperative. The decision-making process pertaining to the selection of appropriate regularization terms assumes a pivotal role, significantly influencing the quality of the restoration outcome. Our research presents a novel model that integrates total fractional-order variation regularization to enhance images while utilizing classical total variation for handling blur kernels. By leveraging the unique characteristics of fractional-order regularization, such as its ability to preserve crucial image elements like edges, corners, and texture, our approach offers significant advantages. We delve into a comprehensive theoretical analysis of the method’s convergence behavior and propose an alternative minimization (AM) algorithm tailored to compute an optimal solution. Numerical experimentation demonstrates that our model yields competitive outcomes, both in visual and quantitative terms, compared to some available well-known approaches.