Current Density Reconstructions Using the L1 Norm

Wagner, Michael; Wischmann, H.‐A.; Fuchs, Manfred; Köhler, Thomas; Drenckhahn, R.

doi:10.1007/978-1-4612-1260-7_96

Cited by 23 publications

(32 citation statements)

References 3 publications

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“…The MNE algorithms produce low resolution solutions of cortical sources spreading over multiple cortical sulci and gyri, which do not reflect the generally sparse and compact nature of most cortical activations evidenced by functional magnetic resonance imaging (fMRI) data. In an attempt to produce more physiologically plausible images than can be obtained using the MNE, the generalized minimum norm estimate (GMNE) algorithms using the L1-norm instead of the L2-norm have been explored (Matsuura and Okabe, 1995; Wagner et al, 1998; Uutela et al, 1999). The attractiveness of these approaches is that they can be solved by a linear programming (LP) method and the properties of LP guarantee that there exists an optimal solution for which the number of nonzero sources does not exceed the number of measurements and the solutions are therefore guaranteed to be sparse and compact.…”

Section: Introductionmentioning

confidence: 99%

“…In the first attempt of L1-norm GMNE (Matsuura and Okabe, 1995), such discrepancy was simply ignored due to the fact that LP could not handle it. Wagner et al (1998) proposed a new decomposition for a vector source in a coordinate system with 12 or even 20 axes to minimize the orientation discrepancy. The number of axes could theoretically be infinite.…”

Section: Introductionmentioning

confidence: 99%

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Sparse source imaging in electroencephalography with accurate field modeling

Ding¹,

He²

2007

Human Brain Mapping

116

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We have developed a new L1-norm based generalized minimum norm estimate (GMNE) and have fully characterized the concept of sparseness regularization inherited in the proposed algorithm, which is termed as sparse source imaging (SSI). The new SSI algorithm corrects inaccurate source field modeling in previously reported L1-norm GMNEs and proposes that sparseness a priori should only be applied to the regularization term, not to the data term in the formulation of the regularized inverse problem. A new solver to the newly developed SSI has been adopted and known as the second order cone programming (SOCP). The new SSI is assessed by a series of simulations and then evaluated using somatosensory evoked potential (SEP) data with both scalp and subdural recordings in a human subject. The performance of SSI is compared with other L1-norm GMNEs and L2-norm GMNEs using three evaluation metrics, i.e. localization error, orientation error, and strength percentage. The present simulation results indicate that the new SSI has significantly improved performance in all evaluation metrics, especially in the metric of orientation error. L2-norm GMNEs show large orientation errors because of the smooth regularization. The previously reported L1-norm GMNEs show large orientation errors due to the inaccurate source field modeling. The SEP source imaging results indicate that SSI has the best accuracy in the prediction of subdural potential field as validated by direct subdural recordings. The new SSI algorithm is also applicable to MEG source imaging.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse source imaging in electroencephalography with accurate field modeling

Ding¹,

He²

2007

Human Brain Mapping

116

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“…The nonlinear L1-norm was used for regularization, minimizing the absolute values, because this norm is known to result to most focal reconstructions (20,41,42). The weighting between the minimum-norm condition and the goodness of fit of the data, Lambda, was iteratively adjusted until a desired fit error of 1/SNR was achieved (X 2 -criterion) (43).…”

Section: Procedures Iv: Current Density Reconstruction (Cdr)mentioning

confidence: 99%

Source Reconstruction of Mesial‐Temporal Epileptiform Activity: Comparison of Inverse Techniques

2000

Epilepsia

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Summary:Purpose: To evaluate whether advanced source reconstruction such as current density reconstruction (CDR) provides additional hints for clinical presurgical evaluation, different source reconstruction techniques with idealized spherical as well as realistically shaped head models (boundary element method, BEM) were applied on interictal and ictal epileptiform activity in presurgical evaluated patients with temporal lobe epilepsy. It is discussed whether CDR and BEM give additional information for presurgical evaluation compared to "conventional" strategies, such as single moving, and spatio-temporal dipole modeling with spherical head models.Methods: A variety of source reconstruction procedures were applied to the data of five patients with pharmacoresistent temporal lobe epilepsy with probable mesial origin: (1) singlemoving dipole in a spherical head model and (2) in BEM, (3) spatio-temporal dipole modeling in a spherical head model and (4) in BEM; and (5) deconvolution with fixed locations and orientations and (6) with cortically constrained L1-norm CDR in BEM. In addition, simulated sources of temporal lobe origin were calculated in each subject with CDR to prove the basic feasibility of this technique in the particular application.Results: Source activity was correctly localized within the affected temporal lobe by all source reconstruction techniques used. Neither single moving dipole, spatio-temporal modeling, nor CDR was able to localize sources at a sublobar level. In the case of two sources, single moving dipole solutions showed changes in dipole orientation in time and spatio-temporal modeling separated two sources, whereas CDR at the peak latency failed to distinguish among different origins. BEM enhanced localization accuracy.Conclusion: There was no advantage of using CDR. Single moving dipole as well as spatio-temporal dipole modeling in BEM leads to more precise localization within the individual anatomy and provides a simple algorithm, which is capable of indicating both the time course and the number of sources.

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“…Under such conditions, the incoherence needs to be computed between measurement supports and signal supports in transform domains (or linear expansion basis functions). While these nice properties of CS have been implemented in problems, such as magnetic resonance imaging (MRI) [16] and radar signals [17], most reported L1-norm regularizations [10,18,19] for EEG/MEG inverse problems search the sparseness in original source domain that often leads to over-focused solutions [20]. Recently, Ding [20] and Chang et al [21] have started to solve EEG/MEG inverse problems using L1-norm regularizations by exploring the sparseness in transform domains, both of which suggest promising inverse imaging characteristics over regular L1-norm regularizations [20].…”

Section: Introductionmentioning

confidence: 99%