Thomas G. Xydis

A filtering approach to the two-dimensional volume conductor forward and inverse problems (biomedical application)

The two-dimensional layered volume conductor forward and inverse problems are solved by modelling the medium as an equivalent two-dimensional filter relating the source and measured potentials. This extends previous results to the multi-dimensional multi-layered case. In principle, the inverse problem can be solved as easily as the forward problem, using 2D FFT algorithms. In fact, it is ill-conditioned and must be regularized. The authors show that Tikhonov regularization, constrained least-squares regularization, and stochastic regularization using a Wiener filter all lead to the same spatial low-pass regularizing filter. New contributions include: (1) extension of the medium filter concept from one to two dimensions; (2) a simple layer-recursive formula for computing the medium filter for a layered medium; and (3) application of various regularization techniques, in the form of regularizing filters, to this problem.

Estimation of locations of bioelectric sources using an equivalent filter

We estimate the number and locations of bioelectric sources in a hor- izontally layered volume conductor. By modelling the extracellular medium as an equivalent filter, the location estimation problem becomes one of estimating param- eters of this equivalent filter, given cursory knowledge of the functional form of the desired sources. The new procedure (1) is computationally efficient, (2) accurately models noise effects on the location estimates, and (3) automatically regularises noisy data. Numerical results are presented, and the Cramer-bo bound for depth esti- mation is derived.

A filtering approach to electrocardiography volume conductor inverse source problems

The authors summarize the application of several signal processing techniques. These include: (1) reconstructing the electrical potential on an active layer of cells from surface measurements using 2-D filtering; (2) identifying locations of still-active layers following myocardial infarction using a multiple-hypothesis generalized likelihood ratio test; and (3) estimating the location of a single still-active layer by maximum likelihood estimation, and determining the Cramer-Rao bound for the mean-square estimator error.<<ETX>>

Estimation of locations of multiple sources in a multi-layer volume conductor using medium filters

An estimate is made of the number and locations of planar bioelectric sources in a horizontally layered volume conductor, from noisy surface measurements of electrical potential on a plane. The effects of the volume conductor are modeled by a medium filter, a 2-D filter which relates the potential on one plane to the potential on another plane; this permits simple regularization. The location estimation problem can then be formulated as a multiple hypothesis minimum error probability generalized likelihood ratio test. Numerical results are presented. The Cramer-Rao bound on the variance of any unbiased depth estimator is discussed to interpret the results.<<ETX>>

Performance bound on depth estimation of bioelectrical source

The unknown depth of bioelectrical sources confined to a horizontal plane in a horizontally layered volume conductor is estimated from noisy measurements of electrical potential on another, parallel plane (e.g. the surface). The Cramer-Rao bound is computed and discussed. Numerical simulation results suggest that the maximum likelihood depth estimate is asymptotically efficient. These results have applications in cardiology, e.g., in determining locations of still-active muscle layers following myocardial infarction.<<ETX>>

Performance bounds on depth estimation of bioelectrical sources

The unknown depth of bioelectrical sources confined to a horizontal plane in a horizontally layered volume conductor is estimated from noisy measurements of electrical potential on another, parallel plane (e.g. the surface). The Cramer-Rao bound is computed and discussed. Numerical simulations suggest the maximum likelihood depth estimate is asymptotically efficient.

A new IIR adaptive filter design using Tellegen's theorem

An IIR (infinite impulse response) adaptive filter algorithm which allows the use of arbitrary network structures is presented. The gradients are derived using a digital network extension of Tellegens theorem which allows the use of exact instantaneous gradients. The algorithm is compared, by simulation, with the IIR LMS (least mean square) algorithm of Widrow (1975) and Stearns (1976).<<ETX>>