Regularization techniques for ill-posed inverse problems in data assimilation

Christopher Budd, Melina A Freitag, N K Nichols

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L 2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L 1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L 1 regularization technique performs more accurately than standard L 2 regularization.
Original languageEnglish
Pages (from-to)168-173
Number of pages6
JournalComputers and Fluids
Volume46
Issue number1
DOIs
Publication statusPublished - Jul 2011

Keywords

  • model error
  • variational data assimilation
  • Tikhonov and L-1 regularization
  • Burgers' equation
  • nonlinear least-squares optimization
  • ill-posed inverse problems

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