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

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