Frames, Sparsity and Image Analysis

at the University of Houston

The Frames, Sparsity and Image Analysis Group consists of a number of professors, postdocs, and graduate students in the mathematics department at the University of Houston who are performing research in several areas of Applied Harmonic Analysis. The Image Analysis Seminar hosts internal and external speakers:

Image Analysis Seminar Schedule

This seminar is open to anyone who wishes to attend or speak.

Some of the major areas of interest include the following:

Multiresolution structures and shearlets in Euclidean spaces
Frames with optimality properties
Sparsity and approximation properties
Applications to biomedical imaging

Members of the Frames, Sparsity and Image Analysis Group

PROFESSORS

Dr. Bernhard Bodmann

Research Areas: Wavelets, Frames, and Image Analysis

Homepage

Publications

Dr. Bodmann is an associate 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 Peter G. Casazza, The road to equal-norm Parseval frames, J. Funct. Anal. 258, 397-420 (2010).
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. Demetrio Labate

Research Areas: Wavelets, Frames, and Image Analysis

Homepage

Curriculum Vitae

Publications

Dr. Labate is an associate professor at the University of Houston. His area of research is harmonic analysis and, specifically, the theory of wavelets and their applications to signal and image processing. His research has been supported by the NSF (National Science Foundation), ARO (Army Research Office), NHARP (Norman Hackerman Advanced Research Program) and GEAR (Grants to Enhance and Advance Research). He was awarded the NSF Career Award in 2008 for his research on shearlets, a novel multiscale directional framework specially designed for the analysis of multidimensional data.

Dr. Manos Papadakis

Research Areas: Wavelets, Frames, and Image Analysis

Homepage

Publications

Dr. Papadakis is an associate 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

Research Areas:		Functional Analysis and Operator Algebras
		Wavelets, Frames, and Image Analysis

Homepage

Curriculum Vitae

Dr. Paulsen is a professor at the University of Houston where he has been a John and Rebecca Moores Professor since 1996. He is an associate editor for the Journal of Operator Theory and has previously served on the editorial boards of Positivity, the Houston Journal of Mathematics, and the Journal of Geometric Analysis. He received a UH Research Excellence Award in 1988, the UH College of Natural Sciences and Mathematics Teaching Excellence Award in 1997, and the university-wide Teaching Excellence Award in 2008. In 2007 he received a Distinguished Alumni Award from his undergraduate institution, Western Michigan University. He has received more than a dozen grants from the NSF since 1983 and directed numerous Ph.D. students. His research interests include operator algebras, completely bounded maps, frames, quantum computation, and function theoretic operator theory. He is the author of 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.

POSTDOCS

Dr. Pooran Negi

Research Areas: Wavelets, Frames, and Image Analysis

Homepage

Publications

Dr. Negi is a former Ph.D. student at UH and a current postdoc working under Dr. Demetrio Labate. His research interests include high-dimensional signal processing and harmonic analysis.

Dr. Pankaj Singh

Research Areas: Wavelets, Frames, and Image Analysis

Homepage

Dr. Singh is a former Ph.D. student at UH and a current postdoc working under Dr. Demetrio Labate. His research interests include frames as codes, error correction, image analysis, and compressed sensing.

GRADUATE STUDENTS

John Haas Advisor: Bernhard Bodmann	Nathan Hammen Advisor: Bernhard Bodmann	Cihan Kayasandik Advisor: Demetrio Labate	Nicole Leonhard Advisor: Vern Paulsen
Ricky Ng Advisor: Vern Paulsen	Carlos Ortiz Advisor: Vern Paulsen	Burcin Ozcan Advisor: Manos Papadakis	Satish Pandey Advisor: Vern Paulsen
Jitendra Prakash Advisor: Vern Paulsen	Sanat Upadhyay Advisor: Manos Papadakis	Da Zheng Advisor: Vern Paulsen

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