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

Freitag, M. A., Nichols, N. ORCID: https://orcid.org/0000-0003-1133-5220 and Budd, C. J. (2010) L1-regularisation for ill-posed problems in variational data assimilation. PAMM - Proceedings in Applied Mathematics and Mechanics, 10 (1). pp. 665-668. ISSN 1617-7061 doi: 10.1002/pamm.201010324

Abstract/Summary

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.