2013/06/07 by A. M. Ebtehaj, Ardeshir Ebtehaj, Milija Županski +5 · 1 citation
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advection #Algorithm #Applied mathematics #Artificial intelligence #Assimilation (phonology) #Computer science #Data assimilation #Image and Signal Denoising Methods #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Meteorology #Norm (philosophy) #Numerical methods in inverse problems #Physics #Regularization (linguistics) #Sobolev space #State variable #Wavelet #physics.data-an
paper · pdf · doi:10.3402/tellusa.v66.21789
published as Tellus A, 66 (2014), no. 21789, 1-17
arxiv created 2013/06/07 · openalex publication_date 2014/02/11 · arxiv updated 2014/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper studies the role of sparse regularisation in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable of interest exhibits sparsity in the real or transform domains. We show that in the presence of sparsity, the ℓ1-norm regularisation produces more accurate and stable solutions than the classic VDA methods. We recast the VDA problem under the ℓ1-norm regularisation into a constrained quadratic programming problem and propose an efficient gradient-based approach, suitable for large-dimensional systems. The proof of concept is examined via assimilation experiments in the wavelet and spectral domain using the linear advection–diffusion equation.