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lp REGULARIZATION FOR ENSEMBLE KALMAN INVERSION
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DOI：10.1137/20M1365168.png)
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Ensemble Kalman inversion (EKI) is a derivative-free optimization method that lies between the deterministic and 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. This paper proposes a strategy to implement l(p), 0 < p <= 1, regularization for EKI to recover sparse structures in the solution. The strategy transforms an lp problem into an l(2) problem, which is then solved by Tikhonov EKI. The transformation is explicit, and thus the proposed approach has a computational cost comparable to Tikhonov EKI. We validate the proposed approach's effectiveness and robustness through a suite of numerical experiments, including compressive sensing and subsurface flow inverse problems.
Keyword:
inverse problems
ensemble Kalman inversion
regularization
sparsity
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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