A new iteratively total variational regularization for nonlinear inverse problems

Abstract

Superior to the other well-known iterations, such as Landweber iteration, total variational regularization is a well-established method for identifying the piecewise smooth parameter and processing the image. Therefore, we propose a new iteratively total variational regularization based on total variational regularization and homotopy perturbation technique in this paper. Taking advantage of Bregman distance, we construct a nested iteration to inverse parameters. Meanwhile we prove that the error of the new method decreases monotonically, and the new iterative method with the noisy data is regular according to the discrepancy principle. In the last numerical section, compared with Landweber type total variational regularization and Runge–Kutta type regularization, numerical results of this new method indicate that this new regularization is time saving for the same accuracy, and more robust to the noisy data.