An automatic regularization parameter selection algorithm in the total variation model for image deblurring

Abstract

Image restoration is an inverse problem that has been widely studied in recent years. The total variation based model by Rudin-Osher-Fatemi (1992) is one of the most effective and well known due to its ability to preserve sharp features in restoration. This paper addresses an important and yet outstanding issue for this model in selection of an optimal regularization parameter, for the case of image deblurring.We propose to compute the optimal regularization parameter along with the restored image in the same variational setting, by considering a Karush Kuhn Tucker (KKT) system. Through establishing analytically the monotonicity result, we can compute this parameter by an iterative algorithm for the KKT system. Such an approach corresponds to solving an equation using discrepancy principle, rather than using discrepancy principle only as a stopping criterion. Numerical experiments can show that the algorithm is efficient and effective for image deblurring problems and yet is competitive to a related selection method.

A New Study of Blind Deconvolution with Implicit Incorporation of Nonnegativity Constraints

“…While there has been work in the parameter selection with nonblind imaging models [51][52][53], further work is required to develop a method for the selection of optimal parameters for both regularisation terms in the blind model.…”

Regularization Parameter Selection for Total Variation Model Based on Local Spectral Response

“…Note that image denoising using GMM is time-consuming, therefore leading to limited applications. For other kinds of selection methods such as LM based method, discrepancy principle based method, generalized cross validation based method, the L/U-curve based method, the structure tensor based method and so on, we refer to [32][33][34][35][36][37][38]. This work concentrates on the regularization estimation using SR.…”

“…A satisfying denoised image can be achieved with selecting a suitable regularization parameter. Many regularization parameter estimation schemes for TV model have been proposed, such as the Lagrange multipliers (LM) based method [8,32], the discrepancy principle based method [33], generalized cross validation based method [34], the L/U-curve based method [35], the structure tensor based method [36,37], the scale space based method [38], and so on.…”

An iterative algorithm for L1-TV constrained regularization in image restoration

“…by a hybrid bisection+secant method [11] yielding a sequence {λ k } converging to the root λ. Usually few bisection iterations are necessary (k s 3) to guarantee the convergence of the secant iterations and globally less than 10 iterations are performed by the hybrid method when stopped by the following criterion: with τ r = τ a = 10 −3 and maxit = 15 in our experiments.…”