A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples

Gallardo, Luis A.; Meju, Max A.; Pérez-Flores, M. A.

doi:10.1088/0266-5611/21/2/002

Cited by 32 publications

(15 citation statements)

References 18 publications

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“…Alternative unnormalized functions based on vector products have been proposed. Remarkably, the cross‐gradient function [ Gallardo and Meju , 2003] defined as has proven useful and stable, and its application has steadily grown in joint multiphysics inverse problems [ Fregoso and Gallardo , 2009; Gallardo and Meju , 2003, 2004; Gallardo et al , 2005; Gallardo , 2007a; Gallardo and Meju , 2007; Hu et al , 2009; Infante et al , 2010; Linde et al , 2006, 2008; Tryggvason and Linde , 2006]. The multiplicative character of this function does not demand additional normalizations/equalizations or angular transformations.…”

Section: Solution Of Multiphysics Inverse Problems Based On Common Stmentioning

confidence: 99%

Structure‐coupled multiphysics imaging in geophysical sciences

Gallardo

Meju

2011

Reviews of Geophysics

142

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[1] Multiphysics imaging or data inversion is of growing importance in many branches of science and engineering. In geophysical sciences, there is a need for combining information from multiple images acquired using different imaging devices and/or modalities because of the potential for accurate predictions. The major challenges are how to combine disparate data from unrelated physical phenomena, taking into account the different spatial scales of the measurement devices, model complexities, and how to quantify the associated uncertainties. This review paper summarizes the role played by the structural gradients-based approach for coupling fundamentally different physical fields in (mainly) geophysical inversion, develops further understanding of this approach to guide newcomers to the field, and defines the main challenges and directions for future research that may be useful in other fields of science and engineering.Citation: Gallardo, L. A., and M. A. Meju (2011), Structure-coupled multiphysics imaging in geophysical sciences, Rev.

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Section: Solution Of Multiphysics Inverse Problems Based On Common Stmentioning

confidence: 99%

Structure‐coupled multiphysics imaging in geophysical sciences

Gallardo

Meju

2011

Reviews of Geophysics

142

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“…Joint inversion based on structural coupling using cross-gradient constraints, introduced by Gallardo andMeju (2003, 2004), has been adapted and applied to a wide range of data types (Gallardo and Meju, 2003, 2007Gallardo et al, 2005;Linde et al, 2006;Linde et al, 2008;Tryggvason and Linde, 2006;Gallardo, 2007;Doetsch et al, 2009;Fregoso and Gallardo, 2009;Hu et al, 2009). The normalized cross-gradient function t 0 qr (x, y, z) of two models m q and m r at location x, y, z is (Linde et al, 2008) t 0 qr (x, y, z) ¼…”

Section: Methodsmentioning

confidence: 99%

1. Joint Inversion of Crosshole GPR and Seismic Traveltime Data

Linde¹,

Doetsch²

2010

Advances in Near-Surface Seismology and Ground-Penetrating Radar

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Joint inversion of crosshole ground-penetrating radar and seismic data can improve model resolution and fidelity of the resultant individual models. Model coupling obtained by minimizing or penalizing some measure of structural dissimilarity between models appears to be the most versatile approach because only weak assumptions about petrophysical relationships are required. Nevertheless, experimental results and petrophysical arguments suggest that when porosity variations are weak in saturated unconsolidated environments, then radar wave speed is approximately linearly related to seismic wave speed. Under such circumstances, model coupling also can be achieved by incorporating cross-covariances in the model regularization. In two case studies, structural similarity is imposed by penalizing models for which the model cross-gradients are nonzero. A first case study demonstrates improvements in model resolution by comparing the resulting models with borehole information, whereas a second case study uses point-spread functions. Although radar seismic wavespeed crossplots are very similar for the two case studies, the models plot in different portions of the graph, suggesting variances in porosity. Both examples display a close, quasilinear relationship between radar seismic wave speed in unconsolidated environments that is described rather well by the corresponding lower Hashin-Shtrikman (HS) bounds. Combining crossplots of the joint inversion models with HS bounds can constrain porosity and pore structure better than individual inversion results can.

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“…One method for imposing similarity of two models, used in joint inversion of two different data sets, is to use a cross gradient technique (Gallardo et al, 2005) where the inversion algorithm minimises an objective function including the cross-product of the gradients of each of the two models. Where the gradients are parallel, which happens when the spatial structure is the same, the crossproduct goes to zero.…”

Section: Introductionmentioning

confidence: 99%

Constraining an inversion to follow curving trends in an image

King¹

2018

ASEG Extended Abstracts

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SUMMARYThis paper addresses the question of how to include structural information, for example from a magnetic image, into an airborne electromagnetic (AEM) inversion. The kind of information we are interested in is the trend directions seen in the magnetic image, such as strike directions of dipping bodies, or the shape of palaeochannels.A commonly-used technique for including prior information is to use a model covariance matrix, describing the spatial covariance between different model points. However, these covariances are usually constructed from a stationary covariance function which is dependent on the vector distance between two points, but is the same for the entire model. However, if a palaeochannel is visible in the magnetics, then we know that the AEM model is more likely to be similar along the channel than away from the channel. We therefore wish to construct a covariance matrix that can take curved and branching structure into account.We construct an inhomogeneous covariance matrix from an image by breaking the image up into multiple windows, and then computing an elliptical distance metric in each window, such that distances in the direction of the features in that window are shorter than distances across those features. This collection of distance metrics then allows us to compute, between any two points in the image, a shortest path that curves to follow the directions of trends in the image. Using this curved-path distance allows us to generate a covariance matrix that encourages the inverted model to follow the trends in the image.

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A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples

Cited by 32 publications

References 18 publications

Structure‐coupled multiphysics imaging in geophysical sciences

Structure‐coupled multiphysics imaging in geophysical sciences

1. Joint Inversion of Crosshole GPR and Seismic Traveltime Data

Constraining an inversion to follow curving trends in an image

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