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A steepest descent algorithm for the global minimization of the Tikhonov functional

Ronny Ramlau

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We report on a new iterative approach for finding a global minimizer of the Tikhonov functional with a special class of nonlinear operators F. Assuming that the operator itself can be decomposed into (or approximated by) a sum of a linear and a bilinear operator, we introduce a two-step iteration scheme based on an outer iteration over the regularization parameter α and an inner iteration with a steepest descent method. Finally we present numerical results for the reconstruction of the emission function in single-photon emission computed tomography.


PACS

02.60.Gf Algorithms for functional approximation

87.59.bd Computed radiography

MSC

47A07 Forms (bilinear, sesquilinear, multilinear)

65D15 Algorithms for functional approximation

65F10 Iterative methods for linear systems (See also 65N22)

65F22 Ill-posedness, regularization

Subjects

Computational physics

Medical physics

Dates

Issue 2 (April 2002)

Received 25 September 2001

Published 7 March 2002



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