Parameter selection for total-variation-based image restoration using discrepancy principle

There are two key issues in successfully solving the image restoration problem: 1) estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2) development of efficient numerical techniques for computing the solution. In this paper, we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image. The new approach is based on the total-variation (TV) regularized strategy and Morozov's discrepancy principle. The TV norm is represented by the dual formulation that changes the minimization problem into a minimax problem. A proximal point method is developed to compute the saddle point of the minimax problem. By adjusting the regularization parameter adaptively in each iteration, the solution is guaranteed to satisfy the discrepancy principle. We will give the convergence proof of our algorithm and numerically show that it is better than some state-of-the-art methods in terms of both speed and accuracy.