On weakly bounded noise in ill-posed problems

    Authors

    P. P. B. Eggermont; V. N. LaRiccia;M. Z. Nashed

    Comments

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    Abbreviated Journal Title

    Inverse Probl.

    Keywords

    NONLINEAR TIKHONOV REGULARIZATION; HILBERT SCALES; INVERSE PROBLEMS; CONVERGENCE-RATES; EQUATIONS; PRINCIPLE; Mathematics, Applied; Physics, Mathematical

    Abstract

    We study compact operator equations with noisy data in Hilbert space. Instead of assuming that the error in the data converges strongly to zero, we only assume a type of weak convergence. Under the source conditions that are usually assumed in the presence of convex constraints, we derive optimal convergence rates for convexly constrained Phillips-Tikhonov regularization. We also discuss a version of the Lepskii method for selecting the regularization parameter.

    Journal Title

    Inverse Problems

    Volume

    25

    Issue/Number

    11

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    14

    WOS Identifier

    WOS:000271481500018

    ISSN

    0266-5611

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