Analysis Research Group

Wavelets, Frames, and Signal Processing






Dr. Manos Papadakis
Ph.D., University of Athens in Greece
B.A., University of Athens in Greece
(List of Publications)

Dr. Papadakis is a professor at the University of Houston and co-founder of the UH Institute for Digital Informatics (IDIA).

Through the IDIA, Dr. Papadakis and his colleagues are developing innovative techniques for harnessing data from images to create multidimensional models for use in medicine, geology and aerospace.

Dr. Papadakis's research interests include Wavelet analysis, frame theory, operator algebras, signal and image processing.





Dr. Vern Paulsen
Ph.D., University of Michigan, 1977
B.A., Western Michigan University, 1973
(Curriculum Vita)

Dr. Paulsen is a professor at the University of Houston and holds a distinguished John and Rebecca Moores Scholar chair. He has been the recipient of several NSF grants, and was awarded a UH Research Excellence Award as well as a UH Teaching Excellence Award. Dr. Paulsen's research interests include Operator Algebras, Completely Bounded Maps, and Positivity. He is the author of the the following books and monographs:
  • Completely bounded maps and operator algebras by Vern Paulsen, Cambridge Studies in Advanced Mathematics 78. Cambridge University Press, Cambridge, 2002. xii+300 pp.
  • Categories of operator modules (Morita equivalence and projective modules) by David Blecher, Paul Muhly, and Vern Paulsen, Mem. Amer. Math. Soc. 143 (2000), no. 681, viii+94 pp.
  • Completely bounded maps and dilations by Vern Paulsen, Pitman Research Notes in Mathematics Series 146. Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1986. xii+187 pp.
  • Hilbert modules over function algebras by Ron Douglas and Vern Paulsen, Pitman Research Notes in Mathematics Series, 217. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. vi+130 pp.



Dr. Bernhard Bodmann
Ph.D., University of Florida, 2001
Masters (Diplom), Universität Erlangen, 1997
(List of Publications)

Dr. Bodmann is an assistant professor at the University of Houston. He has been the recipient of grants from NSF and NSERC. His research interests include uncertainty principles in harmonic analysis, the design of frames for the coding of analog signals, wavelet and filter design, and mathematical physics. Selected papers:
  • 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)
  • 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).
  • Bernhard G. Bodmann, Optimal linear transmission by loss-insensitive packet encoding, Appl. Comput. Harmon. Anal. 22, 274-285, (2007).
  • 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).
  • 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).





Dr. Simon Alexander
Ph.D., University of Waterloo, 2005
M.Ma., University of Waterloo, 2001
B.Sc., University of Victoria, 1998
(Curriculum Vita)

Dr. Alexander is an NSERC postdoctoral fellow at the University of Houston. His research is primarily in the area of Image and Signal Processing, with particular interest in applications to medical imaging. These problems typically involve areas of Harmonic and Functional Analysis, Stochastic processes, Machine Learning, and Optimization.






GRADUATE STUDENTS


Saurabh Jain
Advisor: Manos Papadakis

Preeti Singh
Advisor: Vern Paulsen
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Here is a list of former Analysis graduate students.