Choice of Regularization Parameter in Constrained Total Variational Image Restoration Model

Image restoration problem is ill-conditioning and is generally formulated to solve a total-variational based minimization problem. Because of the physics of the underlying image formation process, the intensities of the images lie in a box range. Hence, it is reasonable to add the box constraints in the minimization problem. The minimization problem includes an unknown regularization parameter. We propose a numerical scheme to simultaneous solve the box constrained Total Variation (TV) minimization using primal-dual method and variable splitting method and choose the suitable regularization parameter according to the discrepancy principle. Numerical simulations are used to demonstrate the performance of the proposed method.