An Implicit Iteration Method for Solving Linear Ill-Posed Operator Equations

In this work, we study a new implicit method to computing the solutions of ill-posed linear operator equations of the first kind under the setting of compact operators. The regularization theory can be used to demonstrate the stability and convergence of this scheme. Furthermore, we obtain convergence results and effective stopping criteria according to Morozov's discrepancy principle. The numerical performances are conducted to show the validity of our implicit method and demonstrate its applicability to deblurring problems.