A projection-based approach to general-form Tikhonov regularization

Publication: Research - peer-reviewJournal article – Annual report year: 2007

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A projection-based approach to general-form Tikhonov regularization. / Kilmer, Misha E.; Hansen, Per Christian; Espanol, Malena I.

In: S I A M Journal on Scientific Computing, Vol. 29, No. 1, 2007, p. 315-330.

Publication: Research - peer-reviewJournal article – Annual report year: 2007

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Author

Kilmer, Misha E.; Hansen, Per Christian; Espanol, Malena I. / A projection-based approach to general-form Tikhonov regularization.

In: S I A M Journal on Scientific Computing, Vol. 29, No. 1, 2007, p. 315-330.

Publication: Research - peer-reviewJournal article – Annual report year: 2007

Bibtex

@article{8559151396544d07847c5bb03af83067,
title = "A projection-based approach to general-form Tikhonov regularization",
publisher = "Society for Industrial and Applied Mathematics",
author = "Kilmer, {Misha E.} and Hansen, {Per Christian} and Espanol, {Malena I.}",
year = "2007",
doi = "10.1137/050645592",
volume = "29",
number = "1",
pages = "315--330",
journal = "S I A M Journal on Scientific Computing",
issn = "1064-8275",

}

RIS

TY - JOUR

T1 - A projection-based approach to general-form Tikhonov regularization

A1 - Kilmer,Misha E.

A1 - Hansen,Per Christian

A1 - Espanol,Malena I.

AU - Kilmer,Misha E.

AU - Hansen,Per Christian

AU - Espanol,Malena I.

PB - Society for Industrial and Applied Mathematics

PY - 2007

Y1 - 2007

N2 - We present a projection-based iterative algorithm for computing general-form Tikhonov regularized solutions to the problem minx| Ax-b |2^2+lambda2| Lx |2^2, where the regularization matrix L is not the identity. Our algorithm is designed for the common case where lambda is not known a priori. It is based on a joint bidiagonalization algorithm and is appropriate for large-scale problems when it is computationally infeasible to transform the regularized problem to standard form. By considering the projected problem, we show how estimates of the corresponding optimal regularization parameter can be efficiently obtained. Numerical results illustrate the promise of our projection-based approach.

AB - We present a projection-based iterative algorithm for computing general-form Tikhonov regularized solutions to the problem minx| Ax-b |2^2+lambda2| Lx |2^2, where the regularization matrix L is not the identity. Our algorithm is designed for the common case where lambda is not known a priori. It is based on a joint bidiagonalization algorithm and is appropriate for large-scale problems when it is computationally infeasible to transform the regularized problem to standard form. By considering the projected problem, we show how estimates of the corresponding optimal regularization parameter can be efficiently obtained. Numerical results illustrate the promise of our projection-based approach.

U2 - 10.1137/050645592

DO - 10.1137/050645592

JO - S I A M Journal on Scientific Computing

JF - S I A M Journal on Scientific Computing

SN - 1064-8275

IS - 1

VL - 29

SP - 315

EP - 330

ER -