An implicit iteration method for solving linear ill-posed operator equations
Tahar Bechouat
Mohammed Cherif Messaadia University, Souk Ahras, Algeria
Keywords: ill-posed problem, operator equation of first kind, iterative regularization, image deblurring
Abstract
In this work, we study a new implicit method to compute 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. Numerical performances are calculated to show the validity of our implicit method and demonstrate its applicability to deblurring problems.
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