Bayesian solutions and performance analysis in bioelectric inverse problems

In bioelectric inverse problems, one seeks to recover bioelectric sources from remote measurements using a mathematical model that relates the sources to the measurements. Due to attenuation and spatial smoothing in the medium between the sources and the measurements, bioelectric inverse problems are generally ill-posed. Bayesian methodology has received increasing attention recently to combat this ill-posedness, since it offers a general formulation of regularization constraints and additionally provides statistical performance analysis tools. These tools include the estimation error covariance and the marginal probability density of the measurements (known as the "evidence") that allow one to predictively quantify and compare experimental designs. These performance analysis tools have been previously applied in inverse electroencephalography and magnetoencephalography, but only in relatively simple scenarios. The main motivation here was to extend the utility of Bayesian estimation techniques and performance analysis tools in bioelectric inverse problems, with a particular focus on electrocardiography. In a simulation study we first investigated whether Bayesian error covariance, computed without knowledge of the true sources and based on instead statistical assumptions, accurately predicted the actual reconstruction error. Our study showed that error variance was a reasonably reliable qualitative and quantitative predictor of estimation performance even when there was error in the prior model. We also examined whether the evidence statistic accurately predicted relative estimation performance when distinct priors were used. In a simple scenario our results support the hypothesis that the prior model that maximizes the evidence is a good choice for inverse reconstructions.


The effects of geometric errors on inverse ECG solutions using Kalman filter and Bayesian MAP estimation Kalman filtre ve Bayes-MAP ile ters EKG çözümlerinde geometrik hatalarin etkisi
Aydin, Ümit; Serinağaoğlu Doğrusöz, Yeşim (2009-10-27)
Geometric errors in inverse ECG are usually the errors occur in the mathematical model used for solution due to wrong interpretation of heart's position and size, conductivities of organs in the model and electrode positions. In this study the effects of geometric errors in inverse ECG problem for Kalman filter and Bayes-AMP methods are studied Furthermore the method suggested by Kaipio et. al., which assumes that these geometric errors are additive noise and independent of the epicardial potentials, is imp...
Implementation and comparison of reconstruction algorithms for magnetic resonance-electric impedance tomography (mr-eit)
Martin Lorca, Dario; Eyüboğlu, Behçet Murat; Department of Biomedical Engineering (2007)
In magnetic resonance electrical impedance tomography (MR-EIT), crosssectional images of a conductivity distribution are reconstructed. When current is injected to a conductor, it generates a magnetic field, which can be measured by a magnetic resonance imaging (MRI) scanner. MR-EIT reconstruction algorithms can be grouped into two: current density based reconstruction algorithms (Type-I) and magnetic flux density based reconstruction algorithms (Type-II). The aim of this study is to implement a series of r...
ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging
Erenler, T; Serinağaoğlu Doğrusöz, Yeşim (Springer Science and Business Media LLC, 2019-10-01)
In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represe...
A Kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem
Aydin, Umit; Serinağaoğlu Doğrusöz, Yeşim (Springer Science and Business Media LLC, 2011-09-01)
In this article, we aimed to reduce the effects of geometric errors and measurement noise on the inverse problem of Electrocardiography (ECG) solutions. We used the Kalman filter to solve the inverse problem in terms of epicardial potential distributions. The geometric errors were introduced into the problem via wrong determination of the size and location of the heart in simulations. An error model, which is called the enhanced error model (EEM), was modified to be used in inverse problem of ECG to compens...
Performance evaluation of current density based magnetic resonance electrical impedance tomography reconstruction algorithms (mr-eit)
Boyacıoğlu, Rasim; Eyüboğlu, Behçet Murat; Department of Biomedical Engineering (2009)
Magnetic Resonance Electrical Impedance Tomography (MREIT) reconstructs conductivity distribution with internal current density (MRCDI) and boundary voltage measurements. There are many algorithms proposed for the solution of MREIT inverse problem which can be divided into two groups: Current density (J) and magnetic flux density (B) based reconstruction algorithms. In this thesis, J-based MREIT reconstruction algorithms are implemented and optimized with modifications. These algorithms are simulated with f...
Citation Formats
Y. Serinağaoğlu Doğrusöz and R. MacLeod, “Bayesian solutions and performance analysis in bioelectric inverse problems,” IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, pp. 1009–1020, 2005, Accessed: 00, 2020. [Online]. Available: