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$l_p$ regularization for ensemble Kalman inversion · Around

2020

$l_p$ regularization for ensemble Kalman inversion

Lee, Yoonsang

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Ensemble Kalman inversion (EKI) is a derivative-free optimization method that lies between the deterministic and the probabilistic approaches for inverse problems.

EKI iterates the Kalman update of ensemble-based Kalman filters, whose ensemble converges to a minimizer of an objective function.
EKI regularizes ill-posed problems by restricting the ensemble to the linear span of the initial ensemble, or by iterating regularization with early stopping.
Another regularization approach for EKI, Tikhonov EKI, penalizes the objective function using the $l_2$ penalty term, preventing overfitting in the standard EKI.

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arXiv:1911.02424
Original
N. K. Chada and X. T. Tong · 1911
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