A Sobolev space analysis of linear regularization methods for ill-posed problems (Q2724860)
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scientific article; zbMATH DE number 1618301
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Sobolev space analysis of linear regularization methods for ill-posed problems |
scientific article; zbMATH DE number 1618301 |
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A Sobolev space analysis of linear regularization methods for ill-posed problems (English)
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12 July 2001
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regularization methods
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linear ill-posed problems
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Sobolev scales
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smoothing
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generalized inverse
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Tikhonov-Phillips regularization
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Radon transform
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computerized tomography
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0.9435035
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0.93567365
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0.93517053
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0.93335634
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0.9248813
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The authors transfer the main results of \textit{A. K. Louis'} unified approach to regularization methods for linear ill-posed problems [Inverse Problems 15, No. 2, 489-498 (1999; Zbl 0933.65060)] to the context of Sobolev scales. They show that the regularization methods may be alternately viewed as smoothing the generalized inverse or applying the (extended) generalized inverse to smoothed data. Conditions for order optimality of the methods are derived and the scheme is illustrated by interpreting it for Tikhonov-Phillips regularization applied to inversion of the Radon transform in computerized tomography.
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