Nonlinear Inverse Problems

Aster, R. C.; Borchers, Brian; Thurber, Clifford H.

doi:10.1016/b978-0-12-804651-7.00015-8

Cited by 201 publications

(206 citation statements)

References 8 publications

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“…To preserve the transitional edges in the signal, we adopted a total variation denoising (TVD) technique. In comparison to Tikhonov regularization, this ℓ 1 -norm regularization technique is superior in preserving edges without over-penalizing the discontinuity of the signal, thus it does not have the edge smoothing effect of Tikhonov regularization [ 20 ]. The TVD method minimizes the difference between a noisy signal y [ n ] and a true signal x [ n ] while trying to preserve the edge of the noisy signal.…”

Section: Proposed Methodsmentioning

confidence: 99%

Improving temporal accuracy of human metabolic chambers for dynamic metabolic studies

et al. 2018

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Metabolic chambers are powerful tools for assessing human energy expenditure, providing flexibility and comfort for the subjects in a near free-living environment. However, the flexibility offered by the large living room size creates challenges in the assessment of dynamic human metabolic signals—such as those generated during high-intensity interval training and short-term involuntary physical activities—with sufficient temporal accuracy. Therefore, this paper presents methods to improve the temporal accuracy of metabolic chambers. The proposed methods include 1) adopting a shortest possible step size, here one minute, to compute the finite derivative terms for the metabolic rate calculation, and 2) applying a robust noise reduction method—total variation denoising—to minimize the large noise generated by the short derivative term whilst preserving the transient edges of the dynamic metabolic signals. Validated against 24-hour gas infusion tests, the proposed method reconstructs dynamic metabolic signals with the best temporal accuracy among state-of-the-art approaches, achieving a root mean square error of 0.27 kcal/min (18.8 J/s), while maintaining a low cumulative error in 24-hour total energy expenditure of less than 45 kcal/day (188280 J/day). When applied to a human exercise session, the proposed methods also show the best performance in terms of recovering the dynamics of exercise energy expenditure. Overall, the proposed methods improve the temporal resolution of the chamber system, enabling metabolic studies involving dynamic signals such as short interval exercises to carry out the metabolic chambers.

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Section: Proposed Methodsmentioning

confidence: 99%

Improving temporal accuracy of human metabolic chambers for dynamic metabolic studies

et al. 2018

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“…in which A is the design matrix, b and x are the observation and model parameters, l is a regularization parameter that determines the amount of regularization and I is the identity matrix. For more information about the Tikhonov Regularization method, the reader is referred to Aster et al (2011). For the problem of interest, it can be seen that the dimensions of the system matrix in Equation 20is ð3n c þ 3n p Þ Â ð3n c þ 3n p Þ in which n c and n p represent the number of unknown coefficients and the coordinates of boundary points on magma chamber, respectively.…”

Section: Application Of Inverse Mfs In Determination Of Magma Sourcementioning

confidence: 99%

The Method of Fundamental Solutions for Solving the Inverse Problem of Magma Source Characterization

Yazdanparast

Voosoghi

Mossaiby

2019

Geomatics, Natural Hazards and Risk

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Volcano is one of the geodynamic phenomena causing irreparable damages. As lava accumulates in reservoir and then comes to the surface, geometry of the source can be used to predict volcanic eruptions. In this study, using the inverse method of fundamental solutions (MFS) and taking into account the effect of topography, the geometry of the source including shape, depth and centre position of the magma tank is estimated. The MFS is a numerical method for solving boundary value problems with known partial differential equations. The displacement field calculated in the previous studies using InSAR for deflation mode of Cerro Blanco volcano was utilized in this study. It was estimated that the magma source of the volcano is a sphere with a radius of 1 km located at a horizontal position of (1:00164eÀ6; À1:00161eÀ6) km and the depth of about 10 km from the summit with respect to the defined coordinate system. This finding is consistent with that of recent studies in which inversion of InSAR data was used to analyse the geometry of the magma source. The RMSE between the deformation fields of the magma source calculated in the previous studies and that of the study herein via MFS was approximately 3 mm.

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“…For inverting DC data, Møller et al (2001) invoke a Bayesian viewpoint following Tarantola and Valette (1982). In this study, we use a weighted sum of a data misfit L 2 -norm and standard smoothness constraints (Menke, 1989;Aster et al, 2005).…”

Section: Continuous Space Domain Formulationmentioning

confidence: 99%

“…for each spectral number (k x ; k y ) is equivalent to an ordinary least-squares problem (Aster et al, 2005) and can be written as…”

Section: Continuous Space Domain Formulationmentioning

confidence: 99%

Fast 3D multichannel deconvolution of electromagnetic induction loop-loop apparent conductivity data sets acquired at low induction numbers

et al. 2017

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Nonlinear Inverse Problems

Cited by 201 publications

References 8 publications

Improving temporal accuracy of human metabolic chambers for dynamic metabolic studies

Improving temporal accuracy of human metabolic chambers for dynamic metabolic studies

The Method of Fundamental Solutions for Solving the Inverse Problem of Magma Source Characterization

Fast 3D multichannel deconvolution of electromagnetic induction loop-loop apparent conductivity data sets acquired at low induction numbers

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