L1-regularisation for ill-posed problems in variational data assimilation

Melina A Freitag, N K Nichols, Christopher J Budd

Research output: Contribution to journalArticle

Abstract

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.
Original languageEnglish
Pages (from-to)665 -668
Number of pages4
JournalPAMM - Proceedings in Applied Mathematics and Mechanics
Volume10
Issue number1
DOIs
Publication statusPublished - Dec 2010

Fingerprint

data assimilation
inverse problem
norm

Cite this

L1-regularisation for ill-posed problems in variational data assimilation. / Freitag, Melina A; Nichols, N K; Budd, Christopher J.

In: PAMM - Proceedings in Applied Mathematics and Mechanics, Vol. 10, No. 1, 12.2010, p. 665 -668.

Research output: Contribution to journalArticle

@article{01d9c46a53414fff96e61314c946f15b,
title = "L1-regularisation for ill-posed problems in variational data assimilation",
abstract = "We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.",
author = "Freitag, {Melina A} and Nichols, {N K} and Budd, {Christopher J}",
note = "PAMM Special Issue: 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Karlsruhe 2010; Editor: Prof. Christian Wieners",
year = "2010",
month = "12",
doi = "10.1002/pamm.201010324",
language = "English",
volume = "10",
pages = "665 --668",
journal = "PAMM - Proceedings in Applied Mathematics and Mechanics",
issn = "1617-7061",
number = "1",

}

TY - JOUR

T1 - L1-regularisation for ill-posed problems in variational data assimilation

AU - Freitag, Melina A

AU - Nichols, N K

AU - Budd, Christopher J

N1 - PAMM Special Issue: 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Karlsruhe 2010; Editor: Prof. Christian Wieners

PY - 2010/12

Y1 - 2010/12

N2 - We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

AB - We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

UR - http://dx.doi.org/10.1002/pamm.201010324

U2 - 10.1002/pamm.201010324

DO - 10.1002/pamm.201010324

M3 - Article

VL - 10

SP - 665

EP - 668

JO - PAMM - Proceedings in Applied Mathematics and Mechanics

JF - PAMM - Proceedings in Applied Mathematics and Mechanics

SN - 1617-7061

IS - 1

ER -