ON THE KANTOROVICH THEOREM AND THE REGULARIZATION OF TOTAL VARIATION DENOISING PROBLEMS

摘要

Total variation methods are an optimizationbased approach for solving image restoration problems. The mathematical formulation results in an equality constrained optimization problem, a solution which can be obtained using Newton's method. This note is motivated by the numerical results of an augmented Lagrangian homotopy method for the regularization of total variation problems. The numerical technique uses the regularization parameter as a homotopy parameter which is reduced. As a result, a sequence of equality constrained optimization problems is solved using Newton's method. In this report, the convergence of an augmented Lagrangian homotopy method for total variation minimization is addressed. We present a relationship between the homotopy parameter and the radius of the Kantorovich ball.