Full Waveform Inversion with Adaptive Regularization

Abstract

Regularization is necessary for solving nonlinear ill-posed inverse problems arising in different fields of geosciences. The base of a suitable regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive (data-driven). In this paper, we propose general black-box regularization algorithms for solving nonlinear inverse problems such as full-waveform inversion (FWI), which admit empirical priors that are determined adaptively by sophisticated denoising algorithms. The nonlinear inverse problem is solved by a proximal Newton method, which generalizes the traditional Newton step in such a way to involve the gradients/subgradients of a (possibly non-differentiable) regularization function through operator splitting and proximal mappings. Furthermore, it requires to account for the Hessian matrix in the regularized least-squares optimization problem. We propose two different splitting algorithms for this task. In the first, we compute the Newton search direction with an iterative method based upon the first-order generalized iterative shrinkage-thresholding algorithm (ISTA), and hence Newton-ISTA (NISTA). The iterations require only Hessian-vector products to compute the gradient step of the quadratic approximation of the nonlinear objective function. The second relies on the alternating direction method of multipliers (ADMM), and hence Newton-ADMM (NADMM), where the least-square optimization subproblem and the regularization subproblem in the composite are decoupled through auxiliary variable and solved in an alternating mode. We compare NISTA and NADMM numerically by solving full-waveform inversion with BM3D regularizations. The tests show promising results obtained by both algorithms. However, NADMM shows a faster convergence rate than Newton-ISTA when using L-BFGS to solve the Newton system.

References in corpus (7)

• BM3D Frames and Variational Image Deblurring
• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• A penalty method for PDE-constrained optimization in inverse problems
• Improving full waveform inversion by wavefield reconstruction with the alternating direction method of multipliers
• Compound Regularization of Full-waveform Inversion for Imaging Piecewise Media
• Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media
• ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization

Cited by in corpus (4)

• Extended full waveform inversion in the time domain by the augmented Lagrangian method
• Efficient extended-search space full-waveform inversion with unknown source signatures
• Inexact Augmented Lagrangian Method-Based Full-waveform Inversion with Randomized Singular Value Decomposition
• Randomized source sketching for full waveform inversion