Non-blind constraint image deblurring problem with mean curvature functional

Most of the time, while deblurring an image, we need the restored image’s intensities to be precisely non-negative. However, it has been noted that using current numerical techniques to solve the problem could produce outcomes that are not always favorable. In restored images, these negative intensities produce a sizable amount of dark space. In this study, we provide a model for the non-blind, mean curvature-based image deblurring problem. The suggested model limits the top boundary of the image intensity values, keeping them within a specified range, in addition to guaranteeing a strictly positive result. Removing of negative intensities or keeping them in prescribed range also help in increasing the quality of deblurred images. The main idea of this paper is to convert the mean curvature based constrained image deblurring problem into an unconstrained one by introducing a Lagrange multiplier. New numerical algorithms are described and compared with the currently used numerical techniques in order to solve the resulting non-linear partial differential equations. Furthermore, a new circulant preconditioned matrix is introduced to overcome the problem of slow convergence when employing a generalized minimal residual method inside of the augmented Lagrangian method. The viability of our suggested approach is demonstrated on test problems.