Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new ...edition maintains the accessible and succinct manner for which it is known, with the addition of: MATLAB examples and problem setsAdvanced color graphicsCoverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervalsOnline data sets and MATLAB scripts that can be used as an inverse theory tutorial.
Additional material on probability, including Bayesian influence, probability density function, and metropolis algorithmDetailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studiesNumerous examples and end-of-chapter homework problems help you explore and further understand the ideas presentedUse as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructorsCheck out the companion website: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123971609 and the Instructor website: http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123971609
Abstract
Impedance inversion of post-stack seismic data is a key technology in reservoir prediction and characterization. Compared to the common used single-trace impedance inversion, multi-trace ...impedance simultaneous inversion has many advantages. For example, it can take lateral regularization constraint to improve the lateral stability and resolution. We propose to use the L
2,0
-norm of multi-trace impedance model as a regularization constraint in multi-trace impedance inversion in this paper. L
2,0
-norm is a joint-sparse measure, which can not only measure the conventional vertical sparsity with L
0
-norm in vertical direction, but also measure the lateral continuity with L
2
-norm in lateral direction. Then, we use a split Bregman iteration strategy to solve the L
2,0
-norm joint-sparse constrained objective function. Next, we use a 2D numerical model and a real seismic data section to test the efficacy of the proposed method. The results show that the inverted impedance from the L
2,0
-norm constraint inversion has higher lateral stability and resolution compared to the inverted impedance from the conventional sparse constraint impedance inversion.
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Sparse level-set formulations allow practitioners to find the minimum 1-norm solution subject to likelihood constraints. Prior art requires this constraint to be convex. Extending these approaches to ...nonconvex likelihood constraints enables outlier robust methods. In this letter, we develop an efficient approach for nonconvex likelihoods, using Regula Falsi root-finding techniques to solve the level-set formulation. Regula Falsi methods are simple, derivative-free and efficient. The approach provably extends level-set methods to the broader class of nonconvex inverse problems. Practical performance is illustrated using Formula Omitted-regularized Student's t inversion, which is a nonconvex problem used to develop outlier-robust approaches.
Inverse problems in statistical physics are motivated by the challenges of 'big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual ...procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.
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Regularization by denoising (RED) is an image reconstruction framework that uses an image denoiser as a prior. Recent work has shown the state-of-the-art performance of RED with learned denoisers ...corresponding to pre-trained convolutional neural nets (CNNs). In this work, we propose to broaden the current denoiser-centric view of RED by considering priors corresponding to networks trained for more general artifact-removal. The key benefit of the proposed family of algorithms, called regularization by artifact-removal (RARE) , is that it can leverage priors learned on datasets containing only undersampled measurements. This makes RARE applicable to problems where it is practically impossible to have fully-sampled groundtruth data for training. We validate RARE on both simulated and experimentally collected data by reconstructing a free-breathing whole-body 3D MRIs into ten respiratory phases from heavily undersampled k-space measurements. Our results corroborate the potential of learning regularizers for iterative inversion directly on undersampled and noisy measurements.
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference ...formulation: given observational data and their uncertainty, the governing forward problem and its uncertainty, and a prior probability distribution describing uncertainty in the parameter field, find the posterior probability distribution over the parameter field. The prior must be chosen appropriately in order to guarantee well-posedness of the infinite-dimensional inverse problem and facilitate computation of the posterior. Furthermore, straightforward discretizations may not lead to convergent approximations of the infinite-dimensional problem. And finally, solution of the discretized inverse problem via explicit construction of the covariance matrix is prohibitive due to the need to solve the forward problem as many times as there are parameters. Our computational framework builds on the infinite-dimensional formulation proposed by Stuart Acta Numer., 19 (2010), pp. 451--559 and incorporates a number of components aimed at ensuring a convergent discretization of the underlying infinite-dimensional inverse problem. The framework additionally incorporates algorithms for manipulating the prior, constructing a low rank approximation of the data-informed component of the posterior covariance operator, and exploring the posterior that together ensure scalability of the entire framework to very high parameter dimensions. We demonstrate this computational framework on the Bayesian solution of an inverse problem in three-dimensional global seismic wave propagation with hundreds of thousands of parameters. PUBLICATION ABSTRACT
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![[Formula Omitted]-Norm Mini...](http://api.summon.serialssolutions.com/2.0.0/image/issn/XR4PS5YY4K/1070-9908/small "[Formula Omitted]-Norm Minimization With Regula Falsi Type Root Finding Methods")
