Non-linear least-squares inversion with data-driven Bayesian regularization
نویسندگان
چکیده
The non-linear inverse problem is formulated in a Bayesian framework. The multivariate normal distribution is assumed in both the noise and prior distributions. However, only the structures of the covariance matrices have to be specified, estimation of the variance levels is included in the inversion procedure. The maximum a posteriori approximation is derived, and the final result is a weighted least-squares inversion algorithm with the ratio between the variance levels as an adaptive, data-driven regularization factor, hence the name Bayesian regularization. The algorithm is tested on inversion of seismic reflection amplitudes and compared with the L-curve approach for choosing the regularization parameter. The Bayesian regularization results in a better regularization value in only a fraction of the time.
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