MATHEMATICAL FOUNDATIONS OF ECG MAP RECONSTRUCTION

References

• Taccardi , B. , Riva , D. ,de Ambroggi , L. 1967 . Le elettromappe in varie forme di Insufficienza Coronarica dell'Uomo . Att. Ace. Med. Lombarda 2721.
   Google Scholar
• Taccardi , B. , Riva , D. ,de Ambroggi , L. 1966 . Alterazione della ripolarizzazione ventricolare con elettrocardiogramma normale . Atti XXVII Cong. Soc. It. Cardiologia , vol. 2, p. 24.
   Google Scholar
• de Ambroggi , L. , Marelli , P. , and Taccardi , B. 1975 . Distribuzione dei potenziali cardiaci sulla superficie del tronco durante la ripolarizzazione ventricolare in un gruppo di soggetti anginosi . Boll. Soc. It. Cardiologia , 20 81 – 85 .
   PubMedGoogle Scholar
• Geselowitz , D. B. , and Schmidt , O. H. 1969 . Electrocardiography . In Biological Engineering , ed. H. P. Schwan . New York McGraw-Hill .
   Google Scholar
• Taccardi , B. , de Ambroggi , L. , and Viganotti , C. 1976 . Body surface mapping of heart potentials . In The theoretical basis of electrocardiography , ed. C. V. Nelson, G. B. Geselowitz , p. 436 – 466 . Oxford Clarendon Press .
   Google Scholar
• Wiener , N. 1961 . Cybernetics , ch. 4 , MIT Press .
   Google Scholar
• Yaglom , A. M. 1961 . Second order homogeneous random fields . Fourth Berkeley Symposium on Math. Statistics , 2 593 . Univ. California Press .
   Google Scholar
• Cabrera , E. 1959 . Teoria e Pratica della Elettrocardiografia. Piccin Padova .
   Google Scholar
• Kornreich , F. , et al. 1977 . Multigroups classification by means of multivariate analysis . In Advances in cardiology , ed. H. Abel , vol. 2 , p. 201 – 204 . Basel Karger .
   Google Scholar
• Kornreich , F. , et al. 1977 . An optimal lead system for In Advances in electrocardiology , ed. H. Abel , vol. 2 , p. 198 – 200 , Basel Karger .
   Google Scholar
• Cottini , C. , Dotti , D. , Gatti , E. , and Taccardi , B. A 240 probe instrument for mapping cardiac potentials . Proceedings of the Satellite Symposium of the 25th International Congress on Physiological Sciences , ed. Rijlan , p. 99 – 102 . Brussels Presses Academiques Europeennes .
   Google Scholar
• Geselowitz , D. B. 1971 . Use of multipole expansion to extract significant features of the surface electrocardiograms . IEEE Trans. Computers-Set,p. 1086 .
   Google Scholar
• Arthur , R. M. , Geselowitz , D. B. , Briller , S. A. , and Trost , R. F. 1972 . Quadrupole components of the human surface ECG . Am. Heart J., 83 663 .
   PubMedGoogle Scholar
• Geselowitz , D. B. 1976 . Determination of multipole components . In The theoretical basis of electrocardiography , ed. Nelson and Geselowitz , p. 202 . Oxford Clarendon Press .
   Google Scholar
• Trost , R. F. , Arthur , R. M. , Geselowitz , D. B. , and Briller , S. A. 1977 . A dipole plus quadrupole lead system for human electrocardiography . J. Electrocard. , 10 27 .
   PubMedGoogle Scholar
• Loeve , M. 1946 . Fonctions aleatoires du second ordre . Rev. Sci. 84 195 , 206 .
   Google Scholar
• Karhunen , K. 1947 . Uber lineare Methoden in den wahrschelichkeits-rechung . Ann. Acad. Sci. Fen. 1 3 – 79 .
   Google Scholar
• Cramer , H. 1951 . A contribution to the theory of stochastic processes . Second Berkeley Symposium on Mathematical Statistics , p. 329 – 339 .
   Google Scholar
• Pugachev , V. S. 1966 . Theory of random functions. London Pergamon Press .
   Google Scholar
• Loeve , M. 1960 . Probability theory. New York Van Nostrand .
   Google Scholar
• Favella , L. , Reineri , M. T. , and Righini , G. U. 1969 . On a mathematical procedure for detecting significant parameters in the classification of a statistical ensemble of phenomena and its applications . Kybernetik 5 band, 5 heft, Jan. , 187 – 194 .
   PubMedGoogle Scholar
• Favella , L. , Giolito , P. , Marazio , G. , Rosettani , E. ,Dell' Erba , C. 1970 . Analisi di ECG mediante lo sviluppo di L.K . Applic. Biomed. Elett. 2 88 – 106 .
   Google Scholar
• Horan , L. G. , Flowers , N. C , and Brody , D. A. 1964 . Principal factor waveforms on the thoracic QRS complex . Circ. Res. 15 131 .
   PubMed Web of Science ®Google Scholar
• Horan , L. G. , Flowers , N. C. , Sohi , G. S. , Hand, R. C, and Johnson , C. 1975 . New evidence for inferoposterior myocardial infarction on surface isopotential maps . Am. J. Cardiol. 35 174 .
   Google Scholar
• Young , T. Y. , and Huggins , W. H. 1962 . The intrinsic component theory of electrocardiography . IEEE Trans, on Biomedical Electronics , 9 214 .
   Google Scholar
• Watanabe , S. 1965 . Karhunen-Loeve expansion and factor analysis . Proc. Fourth Prague Conf. on Information Theory.
   Google Scholar
• Kak , A. , Rosenfeld , A. 1976 . Digital picture processing. New York Academic Press .
   Google Scholar
• Barr , R. C , Spach , M. , Herman Giddens , G. S. 1971 . Selection of the number and position of the measuring locations for electrocardiography . IEEE Trans, on Biomedical Engineering 18 125 – 138 .
   PubMedGoogle Scholar
• Favella , L. , Di Leva , A. , et al. 1972 . La minimizzazione del numero di tracce di rilevamento per la ricostruzione completa delle mappe di potenziale toracico in Elettrocardiografia. In Italian . Proceeding of the II National Congress on Cybernetics , Casciana Terme , p. 515 , ed. L. Felici-Pisa , 25 – 27 October.
   Google Scholar
• Favella , L. , Giolito , P. , di Leva , A. 1973 . The compression of information for surface potential maps in electrocardiography and map reconstruction . Conference at the second international congress on electrocardiology , Yerevan , Armenia , U.S.S.R . 21 – 25 Sept.
   Google Scholar
• Favella , L. , di Leva , A. , and Balossino , N. 1974 . La rappresentazione del potenziale Elettrocardiografico di superficie a partire da 16 sonde . Proceedings of the Third National Congress on Cybernetics and Biophysics , p. 341 , ed. L. Felici-Pisa , 3 – 5 October , San Marino .
   Google Scholar
• Favella , L. , Balossino , N. , di Leva , A. , and Reineri , M. T. 1976 . La ricostruzione delle mappe elettrocardiografiche a partire da un numero limitato di sonde . Proceedings of the Fourth National Congress on Cybernetics and Biophysics , p. 347 – 335 , 11 – 13 Oct.
   Google Scholar
• Favella , L. , Balossino , N. , di Leva , A. , and Reineri , M. T. 1977 . A computer system for map reconstruction . Proceedings of the Fourth International Congress on Electrocardiology. Sept. 20 . Balatonfiired , Hungary , p. 221 – 225 .
   Google Scholar
• Favella , L. , Balossino , N. , di Leva , A. , and Reineri , M. T. 1976 . Para-metri globali invarianti per rotazioni nella caratterizzazione delle mappe di potenziale E.C.G . Proceedings of the Fourth National Congress on Cybernetics and Biophysics p. 347 – 355 .
   Google Scholar
• Warren , R. B. 1977 . Ph.D. Thesis, Department of Biomedical Engineering , Duke University , Durham , North Carolina .
   Google Scholar
• Favella , L. , Balossino , N. , and Reineri , M. T. 1978 . On a limited number of leads for the reconstruction of the electrocardiographic surface potential maps and of some invariant diagnostic parameters . Proceedings of the Fourth European Meeting on Cybernetics and Systems Research. March 28 .
   Google Scholar
• Favella , L. , Balossino , N. , di Leva , A. , and Reineri , M. T. 1977 . The reconstruction of the electrocardiographic surface potential maps from a limited number of leads . Proceedings of the European Conference on Electronics EUREL-IEEE 77 , section 4 , p. 442 – 446 , 3–7 May .
   Google Scholar
• Yaglom , A. M. 1962 . An introduction to the theory of stationary random functions. London Prentice Hall .
   Google Scholar
• Sommerfeld , A. 1949 . Partial differential equations in physics. New York Academic Press .
   Google Scholar
• Weyl , H. 1931 . The theory of groups and quantum mechanics , ch. 3 and 4. Dover Publications. 30b. Rose, M. E 1959. Elementary theory of angular momentum. New York Wiley .
   Google Scholar
• Tikhonov , A. , and Arsenin , V. 1974 . Methodes de resolution de prob-lemes mal poses. Ed Moscou .
   Google Scholar
• Foster , M. An application of the Wiener Kolmogorov smoothing theory to matrix inversion . S.I.A.M. J. App. Mathe. , 9 387.
   Google Scholar
• Strand , O. , and Westwater , E. 1968 . Minimum r.m.s. estimation of the numerical solution of the Fredholm integral equation of the first kind . S.I.A.M.J.Num.Ana. 5 287 .
   Google Scholar
• Szego . 1959 . Orthogonal polynomials , ed. American Mathematical Society Colloquium publications , vol. 23 .
   Google Scholar
• Berezin , I. S. , and Zhidkov , N. P. 1965 . Computing Methods , vol. I . New York Pergamon Press .
   Google Scholar
• Krylow , V. I. 1962 . Approximate calculation of integrals. New York MacMiilan .
   Google Scholar