Research Interests
Theory and design of frames and fusion frames with optimality properties. Optimality criteria from geometric or information-theoretic principles.
  1. Optimal and near-optimal subspace arrangements for high-dimensional parallel computing with fusion frames.
  2. Characterization and design of equiangular tight frames.
  3. Frames as codes: Error correction by linear, redundant encoding of analog signals.
  4. Multiresolution methods and statistical analysis for biomedical imaging.
  5. Multiresolution analysis with directional selectivity in multidimensions.
  6. Uncertainty principles in filter design.
  7. Entropy and phase space bounds for coherent state representations in mathematical physics.
    For more details, see a list of key publications with comments.
      Journal publications
      1. Bernhard G. Bodmann and John Haas, Frame potentials and the geometry of frames, J. Fourier Anal. Appl., dx.doi.org/10.1007/s00041-015-9408-z, 40 pp., (2015).
      2. Bernhard G. Bodmann, Gitta Kutyniok and Xiaosheng Zhuang, Gabor shearlets, Appl. Comput. Harmon. Anal. 38, 87-114 (2015).
      3. Bernhard G. Bodmann and Nathaniel Hammen, Stable phase retrieval with low-redundancy frames, Adv. Comp. Math. 41, 317-331 (2015).
      4. Jie Yao, Anne-Cecile Lesage, Bernhard G. Bodmann, Fazle Hussain and Donald J. Kouri, One dimensional acoustic direct nonlinear inversion using the Volterra inverse scattering series, Inverse Problems 30, no. 7, paper ID 075006, 17 pp., (2014).
      5. Bernhard G. Bodmann, Bijan Camp and Dax Mahoney, Binary frames, graphs and erasures, Involve 7, 151-169 (2014).
      6. Jie Yao, Anne-Cecile Lesage, Bernhard G. Bodmann, Fazle Hussain and Donald J. Kouri, Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential, J. Math. Phys. 55 no. 12, paper ID 123512, 15 pp., (2014).
      7. Bernhard G. Bodmann, Random fusion frames are nearly equiangular and tight, Linear Algebra and its Applications 439, 1401-1414 (2013).
      8. Chia-Chun Chou, Mason Biamonte, Bernhard G. Bodmann and Donald J. Kouri, New system-specific coherent states for bound state calculations, J. Phys. A: Math Theor. 45 (2012) 505302 (14pp).
      9. Bernhard G. Bodmann and Christopher L. Liner, Spikes, nodes and aliasing: Signal recovery from the roots of the spectrogram, SIAM J. Appl. Math. 72, 1449-1473 (2012).
      10. Bernhard G. Bodmann, Jameson Cahill and Peter G. Casazza, Fusion frames and the restricted isometry property, Numerical Functional Analysis and Optimization 33, 770-790 (2012).
      11. Anupam Hazra, Robert Rosenbaum, B. Bodmann, Siyuan Cao, Kresimir Josic and Jokubas Ziburkus, Beta adrenergic modulation of spontaneous spatiotemporal activity patterns and synchrony in hyper-excitable hippocampal circuits, J. Neurophysiol. 108, 658-671 (2012).
      12. Bernhard G. Bodmann, Peter G. Casazza, Vern Paulsen and Darrin Speegle, Spanning and Independence properties of frame partitions, Proc. Amer. Math. Soc. 140, 2193-2207 (2012).
      13. Bernhard G. Bodmann and Pankaj K. Singh, Burst Erasures and the Mean-Square Error for Cyclic Parseval Frames, IEEE Trans. Inform. Theory 57, no. 7, 4622-4635 (2011).
      14. Bernhard G. Bodmann}, Peter G. Casazza and Gitta Kutyniok, A quantitative notion of redundancy for finite frames, Appl. Comput. Harmon. Anal. 30, 348-362 (2011).
      15. Christopher L. Liner and Bernhard G. Bodmann, The Wolf ramp: reflection characteristics of a transition layer, Geophysics 75, A31-35 (2010).
      16. Bernhard G. Bodmann and Helen J. Elwood, Complex equiangular Parseval frames and Seidel matrices containing pth roots of unity, Proc. Amer. Math. Soc. 138, 4387-4404 (2010).
      17. Bernhard G. Bodmann and Peter G. Casazza, The road to equal-norm Parseval frames, J. Funct. Anal. 258, 397-420 (2010).
      18. Donald J. Kouri, Thomas Markovich, Nicholas Maxwell, and Bernhard G. Bodmann, The Heisenberg-Weyl Algebra on the Circle and a Related Quantum Mechanical Model for Hindered Rotation, J. Phys. Chem. A 113, 7698-7705 (2009).
      19. Bernhard G. Bodmann, My Le, Matthew Tobin, Letty Reza and Mark Tomforde, Frame theory for binary vector spaces, Involve 2 589-602 (2009).
      20. Radu Balan, Bernhard G. Bodmann, Peter G. Casazza and Dan Edidin, Painless Reconstruction from Magnitudes of Frame Coefficients, J. Fourier Anal. Appl. 15, 488-501 (2009).
      21. Bernhard G. Bodmann, Vern I. Paulsen and M. Tomforde, Equiangular tight frames from complex Seidel matrices containing cube roots of unity, Linear Algebra Appl. 430, 396-417 (2009).
      22. 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 25, 597-613 (2009).
      23. Bernhard G. Bodmann and Stanley P. Lipshitz, Randomly Dithered Quantization and Sigma-Delta Noise Shaping for Finite Frames, Appl. Comput. Harmon. Anal. 25, 367-380 (2008).
      24. 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). 
      25. 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).
      26. 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).
      27. 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).
      28. 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).
      29. Bernhard G.  Bodmann, Optimal linear transmission by loss-insensitive packet encoding, Appl. Comput. Harmon. Anal. 22, 274-285, (2007).
      30. Bernhard G. Bodmann and Vern I. Paulsen, Frame Paths and Error Bounds for Sigma-Delta Quantization, Appl. Comput. Harmon. Anal. 22, 176--197, (2007).
      31. 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).
      32. 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). 
      33. 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).
      34. Bernhard G. Bodmann and Vern I. Paulsen, Frames, graphs and erasures, Linear Algebra Appl. 404, 118-146, (2005).
      35. 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).
      36. Bernhard G. Bodmann. A matching pursuit on the sphere based on the Poisson semigroup. Sampl. Theory Signal Image Process. 2, 191–205, (2003).
      37. 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).
      38. 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).
      39. 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 and book chapters
      1. Bernhard G. Bodmann, Peter G. Casazza, Jesse Peterson, Ihar Smalyanau and Janet Tremain, Fusion frames and unbiased basic sequences, Excursions in Harmonic Analysis 1, 19-34 (2013).
      2. Bernhard G. Bodmann and Pankaj K. Singh, Cyclic Parseval Frames and the Mean-Square Error for Burst Erasures, Proceedings of Sampling Theory and Applications (SampTA'11), Singapore, 2011.
      3. Robert Azencott, Bernhard G. Bodmann, Demetrio Labate, Anando Sen, King Li, Xiaobo Zhou, Searchlight CT: A new reconstruction method for collimated X-ray tomograph, Proceedings of the International Workshop on New Computational Methods for Inverse Problems (NCMIP 2011), Cachan, France, 2011.
      4. Bernhard G. Bodmann, Peter G. Casazza, Vern I. Paulsen and Darrin Speegle, Independence and spanning properties of frame partitions, Oberwolfach report no. 17, 2011.
      5. Bernhard G. Bodmann and Helen J. Elwood, Seidel's legacy and the existence of complex equiangular Parseval frames, in: Proceedings of the 44th Conference on Information Sciences and Systems, Princeton University, NJ, 2010.
      6. Manos Papadakis, Robert Azencott, Bernhard G. Bodmann, Steerlets: a novel tool for rigid-motion covariant multiscale transforms, in: "Wavelets XIII", Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 7446, pp. 74460A/1-10, Bellingham, WA, 2009.
      7. Peter G. Casazza, Steven Senger, Bernhard G. Bodmann, Gitta Kutyniok, A Low Complexity Replacement Scheme for Erased Frame Coefficients, in: "Wavelets XIII", Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 7446, pp. 74460O/1-10, SPIE, Bellingham, WA, 2009.
      8. Gitta Kutyniok, Bernhard G. Bodmann, Erasure-Proof Transmissions: Fusion Frames meet Coding Theory, in: "Wavelets XIII", Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 7446, pp. 74460P/1-11, Bellingham, WA, 2009.
      9. Bernhard G. Bodmann and Peter G. Casazza, When are frames close to equal-norm Parseval frames? In: "Wavelets XIII", Proceedings of the SPIE, D. Van De Ville, V. K. Goyal and M. Papadakis (Eds.), vol. 7446, pp. 744616/1-14, Bellingham, WA, 2009.
      10. Bernhard G. Bodmann, Gitta Kutyniok and Ali Pezeshki, Erasure-proof coding with fusion frames, Proceedings of SampTA'09, B. Torresani and L. Fesquet (Eds.), accessible at www.latp.univ-mrs.fr/SAMPTA09, 2009.
      11. Bernhard G. Bodmann, Peter G. Casazza, Gitta Kutyniok and Steven Senger, Error correction for erasures of quantized frame coefficients, Proceedings of SampTA'09, B. Torresani and L. Fesquet (Eds.), accessible at www.latp.univ-mrs.fr/SAMPTA09, 2009.
      12. 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.
      13. 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.
      14. 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.
      15. 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.
      16. 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.
      17. 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.
      18. 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.
      19. 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.
      20. 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.