基于稀疏正则化的变分资料同化
Variational Data Assimilation via Sparse Regularization
摘要：
本文研究稀疏正则化在变分资料同化（VDA）问题中的作用。具体而言，它侧重于噪声和下采样观测的数据同化，而感兴趣的状态变量在实域或变换域中表现出稀疏性。我们发现，在稀疏性的存在下，$\ell_{1}$ -范数正则化产生更准确和稳定的解决方案比经典的数据同化方法。为了促进所提出的方法的进一步发展，同化实验进行了小波和谱域使用线性对流扩散方程。
英文摘要：
This paper studies the role of sparse regularization 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 transformed domain. We show that in the presence of sparsity, the $\ell_{1}$-norm regularization produces more accurate and stable solutions than the classic data assimilation methods. To motivate further developments of the proposed methodology, assimilation experiments are conducted in the wavelet and spectral domain using the linear advection-diffusion equation.
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