Iterative Lavrentiev regularization for symmetric kernel-driven operator equations: with application to digital image restoration problems

    Authors

    Y. F. Wang; X. F. Gu; T. Yu;S. F. Fan

    Comments

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    Abbreviated Journal Title

    Sci. China Ser. F-Inf. Sci.

    Keywords

    Lavrentiev regularization; iterative implementation; discrepancy; principle; image restoration; TIKHONOV REGULARIZATION; Computer Science, Information Systems

    Abstract

    The symmetric kernel-driven operator equations play an important role in mathematical physics, engineering, atmospheric image processing and remote sensing sciences. Such problems are usually ill-posed in the sense that even if a unique solution exists, the solution need not depend continuously on the input data. One common technique to overcome the difficulty is applying the Tikhonov regularization to the symmetric kernel operator equations, which is more generally called the Lavrentiev regularization. It has been shown that the iterative implementation of the Tikhonov regularization can improve the rate of convergence. Therefore in this paper, we study the iterative Lavrentiev regularization method in a similar way when applying it to symmetric kernel problems which appears frequently in applications, say digital image restoration problems. We first prove the convergence property, and then under the widely used Morozov discrepancy principle(MDP), we prove the regularity of the method. Numerical performance for digital image restoration is included to confirm the theory. It seems that the iterated Lavrentiev regularization with the MDP strategy is appropriate for solving symmetric kernel problems.

    Journal Title

    Science in China Series F-Information Sciences

    Volume

    48

    Issue/Number

    4

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    467

    Last Page

    483

    WOS Identifier

    WOS:000231865400005

    ISSN

    1009-2757

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