Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10051684" target="_blank" >RIV/00216208:11320/10:10051684 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

Popis výsledku v původním jazyce

This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularization. Given apriori estimates on the covariance structure of errors in the measurement data b, and a suitable statistically-chosen regularization parameter, the Tikhonov regularized least squares functional J approximately follows a chi2 distribution with M degrees of freedom. Using the generalized singular value decomposition a regularization parameter can then be found suchthat the resulting J follows this chi2 distribution, see Mead and Renaut (2008). Because the algorithm explicitly relies on the direct solution of the problem obtained using the generalized singular value decomposition it is not practical for large scaleproblems. Here the approach is extended for large scale problems through the use of the Newton iteration in combination with a Golub-Kahan iterative bidiagonalization of the regularized problem.

Název v anglickém jazyce

Regularization parameter estimation for large-scale Tikhonov regularization using a priori information

Popis výsledku anglicky

This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularization. Given apriori estimates on the covariance structure of errors in the measurement data b, and a suitable statistically-chosen regularization parameter, the Tikhonov regularized least squares functional J approximately follows a chi2 distribution with M degrees of freedom. Using the generalized singular value decomposition a regularization parameter can then be found suchthat the resulting J follows this chi2 distribution, see Mead and Renaut (2008). Because the algorithm explicitly relies on the direct solution of the problem obtained using the generalized singular value decomposition it is not practical for large scaleproblems. Here the approach is extended for large scale problems through the use of the Newton iteration in combination with a Golub-Kahan iterative bidiagonalization of the regularized problem.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Statistics and Data Analysis

ISSN

0167-9473

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

—

Kód UT WoS článku

000281333900047

EID výsledku v databázi Scopus

—