Collaborator: R. DeVore
This project has four areas of focus:
Image compression: Wavelet image compression has proved very successful, consistently outperforming JPEG standard image compression on many classes of images. This project attempts to extend theoretical and practical results in several areas: large medical images (e.g., mammograms); three-dimensional isotropic images (medical MRI images); non-isotropic three-dimensional non-isotropic images (hyperspectral satellite imaging); and a new method of image compression we call 2 1/2-dimensional compression for the Visible Human Project.
Noise removal: We are working on theory and applications for wavelet-shrinkage methods in image noise removal, an area originally developed by David Donoho and Iain Johnstone.
Tomographic image reconstruction: The wavelet-shrinkage method for noise removal has been adapted to the wavelet-vaguelette transform, developed by Donoho, and applied to tomographic image reconstruction with extremely noisy data, e.g., PET imaging techniques, to good effect. Lucier is working with a student, Nam-yong Lee, on wavelet theory and practice in this area.
Image smoothing scale spaces: There is an active area of research on nonlinear image smoothing scale spaces, most of which are generated by time-dependent, nonlinear, partial differential equations. Lucier is working with Antonin Chambolle, University of Paris-Dauphine, on a new wavelet-based nonlinear scale space based on wavelet shrinkage.