An Efficient PDE-Based Model for Image Restoration

In this paper, we propose new time-dependent model for solving total variation (TV) minimization problem in image restoration. The main idea is to apply a priori smoothness on the solution image. TV of the image is minimized subject to constraints involving the point spread function (PSF) of the blurring process and the statistics of the noise. The blurring operator provides useful information in restoration. The constraints are implemented using Lagrange's multipliers. The solution is obtained using the gradient-projection method of Rosen. We present proof of the existence, uniqueness and stability of the viscosity solution of our model. The results of our model using explicit numerical schemes are compared with other known image restoration models.