The Resolving Power of Gross Earth Data

Backus, George E.; Gilbert, Freeman

doi:10.1111/j.1365-246x.1968.tb00216.x

Cited by 1,403 publications

(801 citation statements)

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“…The resolution kernel (Backus and Gilbert, 1968;de Peralta Menendez et al, 1997) can play this role. We introduce the resolution kernel, derived by combining Eqs.…”

Section: Resolution Kernelmentioning

confidence: 99%

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

2005

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This paper discusses the location bias and the spatial resolution in the reconstruction of a single dipole source by various spatial filtering techniques used for neuromagnetic imaging. We first analyze the location bias for several representative adaptive and non-adaptive spatial filters using their resolution kernels. This analysis theoretically validates previously reported empirical findings that standardized low-resolution electromagnetic tomography (sLORETA) has no location bias. We also find that the minimum-variance spatial filter does exhibit bias in the reconstructed location of a single source, but that this bias is eliminated by using the normalized lead field. We then focus on the comparison of sLORETA and the lead-field normalized minimum-variance spatial filter, and analyze the effect of noise on source location bias. We find that the signal-to-noise ratio (SNR) in the measurements determines whether the sLORETA reconstruction has source location bias, while the lead-field normalized minimum-variance spatial filter has no location bias even in the presence of noise. Finally, we compare the spatial resolution for sLORETA and the minimum-variance filter, and show that the minimum-variance filter attains much higher resolution than sLORETA does. The results of these analyses are validated by numerical experiments as well as by reconstructions based on two sets of evoked magnetic responses.

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“…The resolution kernel (Backus and Gilbert, 1968;de Peralta Menendez et al, 1997) can play this role. We introduce the resolution kernel, derived by combining Eqs.…”

Section: Resolution Kernelmentioning

confidence: 99%

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

2005

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“…The method used in this work to estimate the resolving power of the data in the 2D problem (Yanovskaya, 1997) generalizes the method proposed by Backus and Gilbert (1968) for the ''averaging length'' in 1D problems. For 2D tomography problems (Yanovskaya et al, 1998), a functional s(x,y) for different orientations of the coordinate system is used in order to determine the sizes of the averaging area along different directions.…”

Section: Tomographic Methodsmentioning

confidence: 99%

“…The method of Yanovskaya and Ditmar is a generalization to two dimensions of the classical one-dimensional method of Backus and Gilbert (1968). The tomographic method estimates a group velocity map U(x) at each period and wave type by minimizing the following misfit function:…”

Section: Tomographic Methodsmentioning

confidence: 99%

Rayleigh wave group velocity tomography in the Aegean area

et al. 2002

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Data from a large-scale experiment which took place in Greece during the period January -July 1997 have been used to investigate the structure of the Aegean area using surface waves. During this experiment, 30 seismic broadband instruments were deployed throughout the whole Greek area. Additional data during the period 1996 -2000 from other temporary networks have been included in the dataset. One hundred eighty-five events with magnitudes 4.0 V M w V 5.5 recorded by these stations have been collected and processed. The individual dispersion curves of the group velocity of Rayleigh waves for each source-station path have been calculated, producing more than 700 paths covering the studied region. These curves have been used to determine Rayleigh group velocity maps using a 2D-tomography method. On the basis of a regionalization of the dispersion measurements, local averaged dispersion curves have been obtained and non-linearly inverted to obtain models of shear-wave velocity versus depth. Since the dispersion curves in the period range 5 s V T V 30 s are mostly affected by the crustal structure, the model velocities are estimated down to a depth of approximately 35 -45 km. The results from the non-linear Hedhehog inversion as applied to a few local dispersion curves show a crustal thickness of approximately 32 km for the Northern Aegean Sea, and a relatively thin crust of approximately 22 -24 km for the Southern Aegean Sea. D

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“…In this approach, a discretization of brain volume into a set of voxels is employed, each of which is considered to be the location of a current vector. In order to obtain a unique solution, various constraints have been suggested in previous studies: as prominent examples we mention optimal resolution (Backus and Gilbert 1968;Grave de Peralta Menendez et al 1997;Grave de Peralta Menendez and Gonzalez Andio 1999), L 2 minimum norm (Hämäläinen and Ilmoniemi 1984), L 1 minimum norm (called 'selective minimum norm') (Matsuura and Okabe 1995) and maximum spatial smoothness (called 'low resolution brain electromagnetic tomography', LORETA) ).…”

Section: Introductionmentioning

confidence: 99%

Recursive penalized least squares solution for dynamical inverse problems of EEG generation

Yamashita

Galka

Ozaki

et al. 2004

Human Brain Mapping

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In this paper we consider the dynamical inverse problem of EEG generation where a specific dynamics for the electrical current distribution is assumed. By casting this problem into a state space representation and assuming a specific class of parametric models for the dynamics, we can impose general spatio-temporal constraints onto the solution. For the purpose of estimating the parameters and evaluating the model, we employ the Akaike Bayesian Information Criterion (ABIC), which is based on the type II likelihood. As a new approach for estimating the current distribution we introduce a method which we call "Dynamic LORETA". A recursive penalized least squares (RPLS) step forms the main element of our implementation. Whereas LORETA exploits exclusively spatial information, Dynamic LORETA exploits both spatial and temporal information, such that it becomes possible to obtain improved i nverse solutions. The performance of the new method is evaluated by application to simulated EEG data, and a considerable improvement over LORETA is found. We also show results for the application to clinical EEG data.

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The Resolving Power of Gross Earth Data

Cited by 1,403 publications

References 10 publications

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction

Rayleigh wave group velocity tomography in the Aegean area

Recursive penalized least squares solution for dynamical inverse problems of EEG generation

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