Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition

Renaut, Rosemary A.; Helmstetter, Anthony; Vatankhah, Saeed

doi:10.1007/s10543-019-00762-7

Cited by 2 publications

(2 citation statements)

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“…So, a proper choice of the regularization factor plays a key role in obtaining a satisfactory solution. Currently, the L-curve method [36], Morozov's discrepancy principle [37], the Unbiased Predictive Risk Estimator [38], and the Bayesian estimator [39] have been developed to estimate the value of the regularization factor. From the literature [36][37][38][39], it can be found that all these methods consume intensive computations [40].…”

Section: Introductionmentioning

confidence: 99%

“…Currently, the L-curve method [36], Morozov's discrepancy principle [37], the Unbiased Predictive Risk Estimator [38], and the Bayesian estimator [39] have been developed to estimate the value of the regularization factor. From the literature [36][37][38][39], it can be found that all these methods consume intensive computations [40]. In order to overcome the above-mentioned problem, multiplicative regularization was proposed in [41] for the inversion of the contrast source.…”

Section: Introductionmentioning

confidence: 99%

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Inversion of Gravity Data with Multiplicative Regularization Using an Improved Adaptive Differential Evolution

Cheng,

Xiao,

et al. 2023

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Differential evolution (DE) is a stochastic optimization technique that imitates the evolution process in nature. This paper uses an improved adaptive differential evolution to solve gravity inversion with multiplicative regularization. Compared with additive regularization, the advantage of multiplicative regularization is that it does not require the regularization parameter in the search process. The contributions in this paper mainly focus on two aspects: accelerating the convergence speed of adaptive DE and balancing the effect of model and data misfits in the objective function. The effectiveness of the proposed inversion method is verified by synthetic and field cases. For the synthetic cases, it is concluded that, based on the obtained results and analysis, the presented DE method is superior and competitive with its original version. Additionally, the designed parameter adaptation for multiplicative regularization is useful for trading off the effect of data and model misfits. For the field cases, two successful applications from China were conducted, and the obtained density source distributions were in accordance with those obtained from drilling wells. The synthetic and practical examples demonstrate that high-quality inversion results can be obtained using improved adaptive differential evolution and multiplicative regularization.

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