Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem

References

• Gulrajani RM. The forward and inverse problems of electrocardiography. IEEE Eng Med Bio. 1998;17(84):101–122.
   Google Scholar
• Consortium for Electrocardiographic Imaging (CEI). 2016. Available from: http://www.ecg-imaging.org/home.
   Google Scholar
• Rudy Y. Noninvasive Electrocardiographic Imaging of Arrhythmogenic Substrates in Humans. Circ Res. 2013;112(5):863–874.
   PubMed Web of Science ®Google Scholar
• CardioInsight. 2016. Available from: http://www.cardioinsight.com/.
   Google Scholar
• Tikhonov AN, Arsenin VY. Solutions of ill-posed problems. New York (NY): Halsted Press; 1977.
   Google Scholar
• Throne RD, Olson LG. The effects of errors in assumed conductivities and geometry on numerical solutions to the inverse problem of electrocardiology. IEEE Trans Biomed Eng. 1995;42(12):1192–1200.
   PubMed Web of Science ®Google Scholar
• Shou G, Xia L, Jiang M, et al. Truncated total least squares: a new regularization method for the solution of ecg inverse problems. IEEE Trans Biomed Eng. 2008;55(4):1327–1335.
   PubMed Web of Science ®Google Scholar
• Jiang M, Xia L, Huang W, et al. The application of subspace preconditioned LSQR algorithm for solving the electrocardiography inverse problem. Med Eng Phys. 2009;31:979–985.
   PubMed Web of Science ®Google Scholar
• Wang D, Kirby RM, MacLeod RS, et al. Inverse electrocardiographic source localization of ischemia: an optimization framework and finite element solution. J Comput Phys. 2013;250:403–424.
   PubMed Web of Science ®Google Scholar
• Potyagaylo D, Cortes EG, Schulze WHW, et al. Binary optimization for source localization in the inverse problem of ECG. Med Biol Eng Comput. 2014;52(9):717–728.
   PubMed Web of Science ®Google Scholar
• Brooks DH, Ahmad GF, MacLeod RS, et al. Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans Biomed Eng. 1999;46(1):3–18.
   PubMed Web of Science ®Google Scholar
• Ahmad GF, Brooks DH, MacLeod RS. An admissible solution approach to inverse electrocardiography. Ann Biomed Eng. 1998;26:278–292.
   PubMed Web of Science ®Google Scholar
• Serinagaoglu Dogrusoz Y, Mazloumi Gavgani A. Genetic algorithm-based regularization parameter estimation for the inverse electrocardiography problem using multiple constraints. Med Biol Eng Comput. 2013;51(4):367–375.
   PubMed Web of Science ®Google Scholar
• van Oosterom A. The use of spatial covariance in computing pericardial potentials. IEEE Trans Biomed Eng. 1999;46(7):778–787.
   PubMed Web of Science ®Google Scholar
• Serinagaoglu Y, Brooks DH, MacLeod RS. Improved performance of Bayesian solutions for inverse electrocardiography using multiple information sources. IEEE Trans Biomed Eng. 2006;53(10):2024–2034.
   PubMed Web of Science ®Google Scholar
• Greensite F. The temporal prior in bioelectromagnetic source imaging problems. IEEE Trans Biomed Eng. 2003;50(10):1152–1159.
   PubMed Web of Science ®Google Scholar
• Onal M, Serinagaoglu Y. Spatio-temporal solutions in inverse electrocardiography. In: 4th European Conference of the International Federation for Medical and Biological Engineering, IFMBE Proceedings. Berlin, Heidelberg: Springer; Vol. 22; 2008. p. 180–183.
   Google Scholar
• Rahimi A, Sapp J, Xu J, et al. Examining the impact of prior models in transmural electrophysiological imaging: a hierarchical multiple-model Bayesian approach. IEEE Trans Med Imaging. 2016;35(1):229–243.
   PubMed Web of Science ®Google Scholar
• Ghodrati A, Brooks DH, Tadmor G, et al. Wavefront-based models for inverse electrocardiography. IEEE Trans Biomed Eng. 2006;53(9):1821–1831.
   PubMed Web of Science ®Google Scholar
• Aydin U, Serinagaoglu Y. A Kalman filter based approach to reduce the effects of geometric errors and the measurement noise in the inverse ECG problem. Med Biol Eng Comput. 2011;49(9):1003–1013.
   PubMed Web of Science ®Google Scholar
• Corrado C, Gerbeau J, Moireau P. Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography. J Comput Phys. 2015;283:271–298.
   Web of Science ®Google Scholar
• Amisaki T, Eguchi S. Pharmacokinetic parameter estimations by minimum relative entropy method. J Pharmacokinet Biopharm. 1995;23(5):479–494.
   PubMedGoogle Scholar
• Woodbury AD, Ulrych TJ. Minimum relative entropy inversion: theory and application to recovering the release history of a groundwater contaminant. Water Resour Res. 1996;32(9):2671–2681.
   Web of Science ®Google Scholar
• Neupauer RM. A comparison of two methods for recovering the release history of a groundwater contamination source [master’s thesis]. Socorro (NM): New Mexico Institute of Mining and Technology; 1999.
   Google Scholar
• Woodbury AD. A FORTRAN program to produce minimum relative entropy distributions. Comput Geosci. 2004;30(1):131–138.
   Web of Science ®Google Scholar
• Propato M, Sarrazy F, Tryby M. Linear algebra and minimum relative entropy to investigate contamination events in drinking water systems. J Water Resour Planning Manage. 2010;136(4):483–492.
   Web of Science ®Google Scholar
• Sun AY, Nicot JP. Inversion of pressure anomaly data for detecting leakage at geologic carbon sequestration sites. Adv Water Resour. 2012;44:20–29.
   Web of Science ®Google Scholar
• Ma D, Wang S, Zhang Z. Hybrid algorithm of minimum relative entropy-particle swarm optimization with adjustment parameters for gas source term identification in atmosphere. Atmos Environ. 2014;94:637–646.
   Web of Science ®Google Scholar
• Zorzi M, Ticozzi F, Ferrante A. Minimum relative entropy for quantum estimation: Feasibility and general solution. IEEE Trans Inf Theory. 2014;60(1):357–367.
   Web of Science ®Google Scholar
• Stanley PC, Pilkington TC, Morrow MN. The effects of thoracic inhomogeneities on the relationship between epicardial and torso potentials. IEEE Trans Biomed Eng. 1986;33(3):273–284.
   PubMed Web of Science ®Google Scholar
• Shore J, Johnson R. Properties of cross-entropy minimization. IEEE Trans Inf Theory. 1981;27(4):472–482.
   Web of Science ®Google Scholar
• Cover TM, Thomas JA. Chapter 9, Elements of information theory. New York (NY): Wiley; 1991.
   Google Scholar
• Shore J. On a relation between maximum likelihood classification and minimum relative-entropy classification (Corresp.). IEEE Trans Inf Theory. 1984;30(6):851–854.
   Web of Science ®Google Scholar
• Neupauer RM, Borchers B. A MATLAB implementation of the minimum relative entropy method for linear inverse problems. Comput Geosci. 2001;27(7):757–762.
   Web of Science ®Google Scholar
• Woodbury AD, Ulrych TJ. Minimum relative entropy: forward probabilistic modeling. Water Resour Res. 1993;29(8):2847–2860.
   Web of Science ®Google Scholar
• Johnson RW. Relative-entropy minimization with uncertain constraints: theory and application to spectrum analysis. In: Smith C, Erickson G, editors. Maximum-entropy and Bayesian spectral analysis and estimation problems. Vol. 21, Fundamental theories of physics. Netherlands: Springer; 1987. p. 57–73.
   Google Scholar
• Hansen PC. Chapter 4, The L-curve and its use in the numerical treatment of inverse problems. Computational inverse problems in electrocardiography. Southampton: WIT press; 2001. p. 119–142.
   Google Scholar
• MacLeod RS, Taccardi B, Lux RL. Electrocardiographic mapping in a realistic torso tank preparation. In: Proceedings of the IEEE EMBS 17th annual International Conference. Montreal, Quebec, Canada: IEEE Press; 1995. p. 245–246.
   Google Scholar
• Kaipio JP, Somersalo E. Statistical inverse problems: discretization, model reduction and inverse crimes. J Comput Appl Math. 2007;198:493–504.
   Web of Science ®Google Scholar
• LR Bear, LK Cheng, IJ LeGrice, et al. Forward problem of electrocardiography, is it solved? Circ Arrhythm Electrophysiol. 2015;8(3):677–684.
   PubMed Web of Science ®Google Scholar
• N Zemzemi, C Dobrzynski, L Bear, et al. Effect of the torso conductivity heterogeneities on the ECGI inverse problem solution. In: Computing in cardiology; 6--9 September 2015; Nice, France; 2016. p. 233–236.
   Google Scholar
• Punshchykova O, Svehlikova J, Tysler M, et al. Influence of torso model complexity on the noninvasive localization of ectopic ventricular activity. Meas Sci Rev. 2016;16(2):96–102.
   Web of Science ®Google Scholar
• Rudy Y. Forward problem of electrocardiography revisited. Circ Arrhythm Electrophysiol. 2015;8(3):526–528.
   PubMed Web of Science ®Google Scholar
• Cluitmans MJM, Peeters RLM, Westra RL, et al. Noninvasive reconstruction of cardiac electrical activity: update on current methods, applications and challenges. Neth Heart J. 2015;23:301–311.
   PubMed Web of Science ®Google Scholar
• CIBC. map3d: interactive scientific visualization tool for bioengineering data. Scientific Computing and Imaging Institute (SCI); 2016. Available from: http://www.sci.utah.edu/cibc/software.html.
   Google Scholar
• Jazwinski AH. Stochastic processes and filtering theory. Mineola (NY): Dover Publications; 2007.
   Google Scholar
• Farina D. Forward and inverse problems of electrocardiography: clinical investigations [dissertation]. Karlsruhe: Universitat Karlsruhe; 2008. ISBN: 9783866442191.
   Google Scholar
• Ramsey M 3rd, Barr RC, Spach MS. Comparison of measured torso potentials with those simulated from epicardial potentials for ventricular depolarization and repolarization in the intact dog. Circ Res. 1977;41(5):660–672.
   PubMed Web of Science ®Google Scholar
• Klepfer RN, Johnson CR, Macleod RS. The effects of inhomogeneities and anisotropies on electrocardiographic fields: a 3-D finite-element study. IEEE Trans Biomed Eng. 1997;44(8):706–719.
   PubMed Web of Science ®Google Scholar
• Ramanathan C, Rudy Y. Electrocardiographic imaging: I. Effect of torso inhomogeneities on noninvasive reconstruction of body surface electrocardiographic potentials. J Cardiovasc Electrophysiol. 2001;12(2):229–240.
   PubMed Web of Science ®Google Scholar
• Ramanathan C, Rudy Y. Electrocardiographic imaging: II. Effect of torso inhomogeneities on noninvasive reconstruction of epicardial potentials, electrograms, and isochrones. J Cardiovasc Electrophysiol. 2001;12(2):241–252.
   PubMed Web of Science ®Google Scholar
• van Oosterom A. A comparison of electrocardiographic imaging based on two source types. Europace. 2014;16:iv120–iv128.
   PubMed Web of Science ®Google Scholar
• Keller DUJ, Weber FM, Seemann G, et al. Ranking the influence of tissue conductivities on forward-calculated ECGs. IEEE Trans Biomed Eng. 2010;57(7):1568–1576.
   PubMed Web of Science ®Google Scholar
• Bertrand C, Ohmi M, Suzuki R, et al. A probabilistic solution to the MEG inverse problem via MCMC methods: the reversible jump and parallel tempering algorithms. IEEE Trans Biomed Eng. 2001;48(5):533–542.
   PubMed Web of Science ®Google Scholar
• Kaipio JP, Kolehmainen V, Somersalo E, et al. Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography. Inverse Probl. 2000;16:1487–1522.
   Web of Science ®Google Scholar
• Ozmen A, Weber G, Batmaz I, et al. RCMARS: robustification of CMARS with different scenarios under polyhedral uncertainty set. Commun Nonlinear Sci Numer Simul. 2011;16:4780–4787.
   Web of Science ®Google Scholar
• Weber G, Batmaz I, Koksal G, et al. CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization. Inverse Probl Sci Eng. 2012;20:371–400.
   Web of Science ®Google Scholar
• Kuter S, Weber GW, Özmen A, et al. Modern applied mathematics for alternative modeling of the atmospheric effects on satellite images. In: Pinto A, Zilberman D, editors. Modeling, dynamics, optimization and bioeconomics I. Springer International Publishing; 2014. p. 469–485.
   Google Scholar
• Kuter S, Weber GW, Akyürek Z, et al. Inversion of top of atmospheric reflectance values by conic multivariate adaptive regression splines. Inverse Probl Sci Eng. 2015;23(4):651–669.
   Web of Science ®Google Scholar
• Özmen A, Batmaz \.{I}, Weber GW. Precipitation modeling by polyhedral RCMARS and comparison with MARS and CMARS. Environ Model Assess. 2014;19(5):425–435.
   Web of Science ®Google Scholar
• Yerlikaya-Özkurt F, Askan A, Weber GW. An alternative approach to the ground motion prediction problem by a non-parametric adaptive regression method. Eng Optim. 2014;46(12):1651–1668.
   Web of Science ®Google Scholar