Department of Mathematics
Bernhard G. Bodmann
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Research Interests
  1. Frames as codes: Error correction by linear, redundant encoding of analog signals. 
  2. Multiresolution methods and statistical analysis for biomedical imaging.
  3. Isotropic Multiresolution Analysis: smooth wavelets and frame scaling functions without directional bias in any number of dimensions.
  4. Uncertainty principles in filter design.
  5. Entropy and phase space bounds for coherent state representations in mathematical physics.
  6. Holomorphic representations and Berezin-Toeplitz operators
  7. Diffusion methods in sampling theory
Journal publications
  1. Manos Papadakis, Bernhard G. Bodmann, Simon K. Alexander, Deborah Vela, Shikha Baid, Alex A. Gittens, Donald J. Kouri, S. David Gertz, Saurabh Jain, Juan R. Romero, Xiao Li, Paul Cherukuri, Dianna D. Cody, Gregory W. Gladish, Ibrahim Aboshady, Jodie L. Conyers, and S. Ward Casscells, Texture-based Tissue Characterization for High-resolution CT Scans of Coronary Arteries, Communications in Numerical Methods in Engineering, to appear (2008).
  2. Bernhard G. Bodmann and Stanley P. Lipshitz, Randomly Dithered Quantization and Sigma-Delta Noise Shaping for Finite Frames, Appl. Comput. Harmon. Anal., to appear (2008)
  3. Bernhard G. Bodmann, David K. Hoffman, Donald J. Kouri and Manos Papadakis,
    Hermite Distributed Approximating Functionals as Almost-Ideal Low-Pass Filters,
    Sampl. Theory Signal Image Process. 7, 15-38 (2007). 
  4. S. David Gertz, Bernhard G. Bodmann, Deborah Vela, Manos Papadakis, Ibrahim Aboshady, Paul Cherukuri, Simon Alexander, Donald J. Kouri, Shikha Baid, Alex A. Gittens, Gregory W. Gladish, Jodie L. Conyers, Dianna D. Cody, Lilach Gavish, Reza M. Mazraeshahi, Wayne T. Wilner, Lorraine Frazier, Mohammad Madjid, Alireza Zarrabi, Serhiy Lukovenkov, Amany Ahmed, James T. Willerson, S. Ward Casscells, Three-dimensional isotropic wavelets for post-acquisitional extraction of latent images of atherosclerotic plaque components from micro-computed tomography of human coronary arteries, Academic Radiology 14, 1509-1519 (2007).
  5. Wayne T. Wilner, Reza M. Mazraeshahi,  Ibrahim F. Aboshady, Bernhard G. Bodmann, M. Papadakis, D. Kouri, Jodie L. Conyers, Paul Cherukuri, Deborah Vela,  Gregory Gladish, Lilach Gavish, Dianna D. Cody, Lorraine Frazier, Serhiy Lukovenkov, Mohamed Madjid, Alireza Zarrabi, Ahmed, A., James T. Willerson, S. Ward Casscells, and S. David Gertz,  Quantification of Roughness of Calcific Deposits in Computed Tomography Scans of Human Coronary Arteries.  Investigative Radiology 42, 771-776 (2007).
  6. Bernhard G. Bodmann, David W. Kribs and Vern I. Paulsen, Decoherence-Insensitive Quantum Communication by Optimal $C^*$-Encoding, IEEE Trans. Inform. Theory 53, 4738-4749 (2007).
  7. Bernhard G. Bodmann, Vern I. Paulsen and Soha Abdulbaki, Smooth frame path termination for higher order sigma-delta quantization, J. Fourier Anal. Appl. 13, 285-307 (2007).
  8. Bernhard G.  Bodmann, Optimal linear transmission by loss-insensitive packet encoding, Appl. Comput. Harmon. Anal. 22, 274-285, (2007).
  9. Bernhard G. Bodmann and Vern I. Paulsen, Frame Paths and Error Bounds for Sigma-Delta Quantization, Appl. Comput. Harmon. Anal. 22, 176--197, (2007).
  10. Bernhard G. Bodmann, Antonios Melas, Manos Papadakis and Theodoros Stavropoulos,  Analog to Digital, Revisited: Controlling the Accuracy of Reconstruction, Sampl. Theory Signal Image Process. 5, 321-340, (2006).
  11. Bernhard G. Bodmann, Manos Papadakis, and Qiyu Sun, An inhomogeneous uncertainty principle for digital low-pass filters, J. Fourier Anal. Appl. 12, 181-211, (2006). 
  12. S. David Gertz, Paul Cherukuri, Bernhard G.  Bodmann, Gregory Gladish, Wayne T.Wilner, Jodie L. Conyers, Ibrahim Aboshady, Mohamed Madjid, Deborah Vela, Serhiy Lukovenkov, Manos Papadakis, Donald J. Kouri, Reza Mohammadi Mazraeshai, Lorraine Frazier, Alireza Zarrabi, Don Elrod, James T. Willerson, and S. Ward Casscells, Usefulness of multidetector computed tomography for noninvasive evaluation of coronary arteries in asymptomatic patients, Am. J. Cardiol. 97, 287-93, (2006).
  13. Bernhard G. Bodmann and Vern I. Paulsen, Frames, graphs and erasures, Linear Algebra Appl. 404, 118-146, (2005).
  14. Bernhard G. Bodmann, A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics, Commun. Math. Phys. 250, 287--300, (2004).
  15. Bernhard G. Bodmann. A matching pursuit on the sphere based on the Poisson semigroup. Sampl. Theory Signal Image Process. 2, 191–205, (2003).
  16. Bernhard G. Bodmann, Construction of Self-Adjoint Berezin-Toeplitz Operators on Kähler Manifolds and a Probabilistic Representation of the Associated Semigroups, J. Geom. Phys. 47, 128-160, (2003).
  17. Bernhard G. Bodmann, A relation of Berezin-Toeplitz operators to Schrödinger operators and the probabilistic representation of Berezin-Toeplitz semigroups, Math. Phys. Anal. Geom. 5,  287-306, (2002).
  18. Bernhard Bodmann, Hajo Leschke and Simone Warzel, A rigorous path integral for quantum
    spin using flat-space Wiener regularization, J. Math. Phys. 40, 2549--2559, (1999).
Conference proceedings
  1. Bernhard G. Bodmann, Peter G. Casazza, Dan Edidin and Radu Balan, Frames for Linear Reconstruction without Phase, in: Proceedings of the 42nd Conference on Information Sciences and Systems, Princeton University, NJ, pp. 721-726, 2008.
  2. Stanley P. Lipshitz, John Vanderkooy and Bernhard G. Bodmann, Sigma-Delta Modulators Without Feedback Around the Quantizer? In: Proceedings of the 123rd Convention of the Audio Engineering Society (October 2007, New York, N.Y.), Paper no. 7201, pp. 1-15, 2007.
  3. Bernhard G. Bodmann, Burst erasures and the mean-square error for cyclic frames, Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 6701, pp. 67011P/1-9, 2007.
  4. Bernhard G. Bodmann and Stanley P. Lipshitz, Random rounding in redundant representations, in "Wavelets XII'', Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 6701, pp. 670103/1-12, 2007.
  5. Radu Balan, Bernhard G. Bodmann, Peter G. Casazza, and Dan Edidin, Fast Algorithms for Signal Reconstruction without Phase, in "Wavelets XII'', Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 6701, pp. 67011L/1-9, 2007.
  6. Bernhard G. Bodmann and Vern I. Paulsen,  Loss-Insensitive vector encoding with two-uniform frames}, in "Wavelets XI'', Proceedings of the SPIE, vol. 5914, M. Papdakis, A. F. Laine, M. A. Unser (Eds.), pp. 591403/1-12, 2005.
  7. B. G. Bodmann, M. Papadakis, D. J. Kouri, S. D. Gertz, P. Cherukuri, D. Vela, G. Gladish, D. Cody,
    I. Aboshady, J. L. Conyers, W. T. Willerson, and S. W. Casscells, Frame Isotropic Multiresolution Analysis for MicroCT Scans of Coronary Arteries, in "Wavelets XI'', Proceedings of the SPIE, vol. 5914, M. Papdakis, A. F. Laine,  M. A. Unser (Eds.), pp. 59141O/1-12, 2005.
  8. Bernhard G. Bodmann and John R. Klauder, Path Integral Quantization for a Toroidal
    Phase Space, in: ``Coherent States, Quantization and Gravity'', Proceedings of the XVIIth Workshop on Geometric Methods in Physics, Warsaw University Press, Warsaw, 2001.
  9. Bernhard G. Bodmann, Hajo Leschke and Simone Warzel, A rigorous path-integral formula for quantum-spin dynamics via planar Brownian motion, in: Proceedings of the Sixth International Conference on Path Integrals from peV to TeV, R. Casalbuoni et al. (Eds.), World Scientific, Singapore, 1999.
Bernhard G. Bodmann,   University of Houston    ---    Last modified:  April 20 2007 - 13:48:50
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