Bradley J. Lucier
Professor Emeritus of Mathematics
Professor Emeritus of Computer Science
Joined department: 1981
Professor Lucier has worked for over twenty 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 is a study of radiologist performance in interpreting wavelet-compressed mammographic images. The compression method was designed specifically to keep image features that are needed to interpret mammograms. The results showed that after compressing the images over 50-to-1 (on average; compression rates ranged from 14-to-1 for mammograms with dense structures to over 2000-to-1 for mammograms with few optical structures) radiologists interpreted the compressed mammograms more accurately than they interpreted the originals. Such effective data compression may allow mammographic screenings to be performed by technicians in areas traditionally underserved by the medical community, with the data sent over regular phone lines to radiologists in medical centers for interpretation.
The second paper introduces a new numerical method for image smoothing based on the total variation norm, as introduced in a famous 1992 paper by Rudin, Osher, and Fatemi. Our new method is more isotropic and exhibits less smoothing than previous methods. Finally, the third paper with my student Jingyue Wang gives the first provable error bounds for Rudin-Osher-Fatemi image smoothing, including the new method introduced in the second paper.
Maria Kallergi, Bradley J. Lucier, Claudia G. Berman, Maria R. Hersh, J. Kim Jihai, Margaret S. Szabunio, and Robert A. Clark, "High-performance wavelet compression for mammography: localization response operating characteristic evaluation", Radiology, 238(1):62-73, 2006
Antonin Chambolle, Stacey E. Levine, and Bradley J. Lucier, "An upwind finite-difference method for total variation-based image smoothing", SIAM Journal on Imaging Sciences, 4(1):277-299, 2011
Jingyue Wang and Bradley J. Lucier, "Error bounds for finite-difference methods for Rudin-Osher-Fatemi image smoothing", SIAM Journal on Numerical Analysis, 49(2):845-868, 2011