CS 2003-2004 Faculty Information - Department of Computer ...

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CS 2003-2004 Faculty Information
Bradley J. Lucier
Education:
B.Sc., Mathematics, University of Windsor, 1976
SM, Applied Mathematics, University of Chicago, 1978
PhD, Applied Mathematics, University of Chicago, 1981
Position:
Professor of Mathematics and Computer Science
Bio-sketch:
Professor Lucier has worked for over ten years on wavelet and multiresolution methods for image processing and other
applications. He has a particular interest in applications in medical imaging (image compression for telemedicine,
tomographic and MRI reconstruction, etc.).
The selected publications below indicate some of these interests. The first paper relates variational problems to wavelet
shrinkage, as introduced by David Donoho and Iain Johnstone. The second paper gives an interpretation of translation-invariant
wavelet shrinkage, introduced by Donoho and Ronald Coifman, as gradient descent along a convex functional;
Gaussian smoothing can be interpreted in the same way (with a different functional).
Finally, the third paper introduces several results about wavelet methods for medical tomography, especially for
Positron Emission Tomography (PET) imaging. Basically, it again puts into a variational framework the waveletvaguelette
method of Donoho; it shows that wide classes of computationally efficient wavelet transforms can be used
for tomography; and it gives examples that show that wavelet techniques are much more effective than the usual filtered
back-projection method for PET imaging.
This work has been supported continuously by the Office of Naval Research since 1990.
Selected Publications:
Antonin Chambolle, Ronald A. DeVore, Namyong Lee, and Bradley J. Lucier,“Nonlinear Wavelet Image Processing:
Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage,” IEEE Transactions on Image
Processing: Special Issue on Partial Differential Equations and Geometry-Driven Diffusion in Image Processing and
Analysis, Volume 7, pp. 319-335, 1998.
Antonin Chambolle and Bradley J. Lucier, “Interpreting Translation-Invariant Wavelet Shrinkage as a New Image
Smoothing Scale Space,” Transactions on Image Processing, Volume 10, pp. 993-1000, 2001.
Namyong Lee and Bradley J. Lucier, “Wavelet Methods for Inverting the Radon Transform with Noisy Data,” IEEE
Transactions on Image Processing, Volume 10, pp. 79-94, 2001.
Robert E. Lynch
Education:
BS, Engineering Physics, Cornell University, 1954
MA, Mathematics, Harvard University, 1961
PhD, Applied Mathematics, Harvard University, 1963
Position:
Professor Emeritus of Computer Science and Mathematics