Bias and multiscale correction methods for variational state estimation

被引:1
作者
Galarce, F. [1 ]
Mura, J. [2 ]
Caiazzo, A. [3 ]
机构
[1] Pontificia Univ Catolica Valparaiso, Sch Civil Engn, Valparaiso, Chile
[2] Univ Tecn Federico Santa Maria, Dept Mech Engn, Santiago, Chile
[3] Leibniz Inst Forschungsverbund Berlin eV WIAS, Weierstrass Inst Angew Anal & Stochast, Berlin, Germany
关键词
Variational state estimation; Data assimilation; Bias correction; Ultrasound images; Medical imaging; Biomedical engineering; DATA ASSIMILATION; ULTRASOUND;
D O I
10.1016/j.apm.2024.115761
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this paper employs variational state estimation using the so-called parametrized-background data-weak method. This approach relies on a background manifold parametrized by a set of constraints, enabling the state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. The proposed formulation incorporates a novel bias correction mechanism and a manifold decomposition that handles rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The method is validated in different examples, including the assimilation of biased synthetic data, discontinuous signals, and Doppler ultrasound data obtained from experimental measurements.
引用
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页数:16
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